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Abstracts of Talks Given at the 8th International Conference on Stochastic Methods Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 A. N. Shiryaev
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 674-711, February 2024. This paper presents abstracts of talks given at the 8th International Conference on Stochastic Methods (ICSM-8), held June 1--8, 2023 at Divnomorskoe (near the town of Gelendzhik) at the Raduga sports and fitness center of the Don State Technical University. This year's conference was dedicated to the 120th birthday
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On Sufficient Conditions in the Marchenko--Pastur Theorem Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 P. A. Yaskov
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 657-673, February 2024. We find general sufficient conditions in the Marchenko--Pastur theorem for high-dimensional sample covariance matrices associated with random vectors, for which the weak concentration property of quadratic forms may not hold in general. The results are obtained by means of a new martingale method, which may be
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On Forward and Backward Kolmogorov Equations for Pure Jump Markov Processes and Their Generalizations Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 E. A. Feinberg, A. N. Shiryaev
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 643-656, February 2024. In the present paper, we first give a survey of the forward and backward Kolmogorov equations for pure jump Markov processes with finite and countable state spaces, and then describe relevant results for the case of Markov processes with values in standard Borel spaces based on results of W. Feller and the authors
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One Limit Theorem for Branching Random Walks Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 N. V. Smorodina, E. B. Yarovaya
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 630-642, February 2024. The foundations of the general theory of Markov random processes were laid by A.N. Kolmogorov. Such processes include, in particular, branching random walks on lattices $\mathbf{Z}^d$, $d \in \mathbf{N}$. In the present paper, we consider a branching random walk where particles may die or produce descendants at
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On Complete Convergence of Moments in Exact Asymptotics under Normal Approximation Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 L. V. Rozovsky
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 622-629, February 2024. For the sums of the form $\overline I_s(\varepsilon) = \sum_{n\geqslant 1} n^{s-r/2}\mathbf{E}|S_n|^r\,\mathbf I[|S_n|\geqslant \varepsilon\,n^\gamma]$, where $S_n = X_1 +\dots + X_n$, $X_n$, $n\geqslant 1$, is a sequence of independent and identically distributed random variables (r.v.'s) $s+1 \geqslant 0$, $r\geqslant
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On a Diffusion Approximation of a Prediction Game Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 M. V. Zhitlukhin
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 607-621, February 2024. This paper is concerned with a dynamic game-theoretic model, where the players place bets on outcomes of random events or random vectors. Our purpose here is to construct a diffusion approximation of the model in the case where all players follow nearly optimal strategies. This approximation is further used to
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Kolmogorov's Last Discovery? (Kolmogorov and Algorithmic Statistics) Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 A. L. Semenov, A. Kh. Shen, N. K. Vereshchagin
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 582-606, February 2024. The definition of descriptional complexity of finite objects suggested by Kolmogorov and other authors in the mid-1960s is now well known. In addition, Kolmogorov pointed out some approaches to a more fine-grained classification of finite objects, such as the resource-bounded complexity (1965), structure function
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Laplace Expansion for Bartlett--Nanda--Pillai Test Statistic and Its Error Bound Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 H. Wakaki, V. V. Ulyanov
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 570-581, February 2024. We construct asymptotic expansions for the distribution function of the Bartlett--Nanda--Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is
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On Symmetrized Chi-Square Tests in Autoregression with Outliers in Data Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 M. V. Boldin
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 559-569, February 2024. A linear stationary model $\mathrm{AR}(p)$ with unknown expectation, coefficients, and the distribution function of innovations $G(x)$ is considered. Autoregression observations contain gross errors (outliers, contaminations). The distribution of contaminations $\Pi$ is unknown, their intensity is $\gamma n^{-1/2}$
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Weakly Supercritical Branching Process in a Random Environment Dying at a Distant Moment Theory Probab. Appl. (IF 0.6) Pub Date : 2024-02-07 V. I. Afanasyev
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 537-558, February 2024. A functional limit theorem is proved for a weakly supercritical branching process in a random environment under the condition that the process becomes extinct after time $n\to \infty $.
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On Nondegenerate Itô Processes with Moderated Drift Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 N. V. Krylov
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 510-536, November 2023. We present an approach to proving parabolic Aleksandrov estimates with mixed norms for stochastic integrals with singular “moderated” drift.
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A Weak Law of Large Numbers for Dependent Random Variables Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 I. Karatzas, W. Schachermayer
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 501-509, November 2023. \bad Each sequence $f_1,f_2,\dots$ of random variables satisfying $\lim_{M\to \infty}(M\sup_{k\in \mathbf N}\mathbf{P}(|f_k|>M))=0$ contains a subsequence $f_{k_1},f_{k_2},\dots$ which, along with all its subsequences, satisfies the weak law of large numbers $\lim_{N\to\infty}\bigl((1/N) \sum^N_{n=1} f_{k_n}-
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Wiener Spiral for Volatility Modeling Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 M. Fukasawa
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 481-500, November 2023. Focusing on a lognormal stochastic volatility model, we present an elementary introduction to rough volatility modeling for financial assets with some new findings.
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On Characterization of Quantum Gaussian Measurement Channels Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 A. S. Holevo
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 473-480, November 2023. We provide a characterization of measurement (quantum-classical) channels, which map Gaussian states to Gaussian probability distributions.
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The Kolmogorov Inequality for the Maximum of the Sum of Random Variables and Its Martingale Analogues Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 N. E. Kordzakhia, A. A. Novikov, A. N. Shiryaev
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 457-472, November 2023. We give a survey of the results related to extensions of the Kolmogorov inequality for the distribution of the absolute value of the maximum of the sum of centered independent random variables to the case of martingales considered at random stopping times.
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On One Family of Random Operators Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 440-456, November 2023. Random operators arising in the construction of probabilistic representation of the resolvent of the operator $-\frac{1}{2}\,\frac{d}{dx}\bigl(b^2(x)\frac{d}{dx}\bigr)$ are considered and shown to be integral with probability $1$. Properties of their kernels are investigated.
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On mm-Entropy of a Banach Space with Gaussian Measure Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 A. M. Vershik, M. A. Lifshits
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 431-439, November 2023. For a broad class of Banach spaces with Gaussian measure, we show that their entropy in the sense of Shannon (the $\mathrm{mm}$-entropy) is closely related to the entropy of the corresponding ellipsoid of concentration and behaves, in a certain range, as the logarithm of the measure of small balls. Relations between
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Population Size of a Critical Branching Process Evolving in an Unfavorable Environment Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 V. A. Vatutin, E. E. Dyakonova
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 411-430, November 2023. Let $\{Z_n,\, n=0,1,\dots\}$ be a critical branching process in a random environment and let $\{S_n,\, n=0,1,\dots\}$ be its associated random walk. It is known that if the distribution of increments of this random walk belongs (without centering) to the domain of attraction of a stable distribution, then there
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On Relevant Features Selection Based on Information Theory Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 A. V. Bulinski
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 392-410, November 2023. It is shown that widely used suboptimal algorithms of feature selection based on information theory concepts do not necessarily identify a collection of features (relevant in a sense) affecting the studied random response. This can be considered as a reflection of the epistasis phenomenon known in genetics, when
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On the Asymptotic Approach to the Change-Point Problem and Exponential Convergence Rate in the Ergodic Theorem for Markov Chains Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 A. A. Borovkov
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 370-391, November 2023. Under the assumption that the change-point time is large, a Poisson approximation for the distribution of the number of false alarms is obtained. We also find upper bounds for the probability of a ``false alarm” on a given time interval. An asymptotic expansion for the mean delay time of the alarm signal relative
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Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 V. I. Bogachev, M. Röckner, S. V. Shaposhnikov
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 342-369, November 2023. The paper gives a survey of several directions of research connected with the works of A.N. Kolmogorov on parabolic and elliptic Fokker--Planck--Kolmogorov equations for transition and stationary probabilities of diffusion processes. We present the fundamental results on existence of solutions, their uniqueness
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On the 120th Birthday of Andrei Nikolaevich Kolmogorov Theory Probab. Appl. (IF 0.6) Pub Date : 2023-11-07 A. N. Shiryaev
Theory of Probability &Its Applications, Volume 68, Issue 3, Page 339-341, November 2023. This article precedes a series of papers dedicated to the 120th anniversary of the birth (on April 25, 1903) of Andrei Nikolaevich Kolmogorov.
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On Student Workshops Organized by the Vega Institute Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 K. Yu. Klimov, M. N. Tsareva
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 337-338, August 2023. This note presents information about three workshops on financial and actuarial mathematics held in 2022 by The Vega Institute Science Promotion Foundation. The goal of the Foundation is to support and develop projects for training highly qualified personnel in the field of financial and actuarial mathematics in
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Seminars, Conferences, Books Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 M. V. Zhitlukhin
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 334-336, August 2023. This note presents information about four remote seminars in probability that are currently ongoing and six in-person conferences that were held in 2022. Also given are synopses of two probability textbooks published in 2022.
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Information on the General Seminar of the Department of Probability, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia, Fall Term 2022 Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 E. B. Yarovaya
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 330-333, August 2023. This paper presents abstracts of talks given at the General Seminar of the Department of Probability, Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, held in Moscow in 2022. Current information about the seminar is available at http://new.math.msu.su/department/probab/seminar.html.
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On Sub-Gaussian Concentration of Missing Mass Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 M. Skorski
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 324-329, August 2023. The statistical inference on missing mass aims to estimate the weight of elements not observed during sampling. Since the pioneer work of Good and Turing, the problem has been studied in many areas, including statistical linguistics, ecology, and machine learning. Proving the sub-Gaussian behavior of the missing
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On the Sum of Gaussian Martingale and an Independent Fractional Brownian Motion Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 R. Belfadli, M. Chadad, M. Erraoui
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 316-323, August 2023. In the same context as in the seminal paper [P. Cheridito, Bernoulli, 7 (2001), pp. 913--934], we are concerned with the semimartingale property of the sum of some Gaussian martingale and an independent fractional Brownian motion with Hurst parameter $H \in (0,1)$. At the same time, we emphasize that the Markov
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Cost Optimization of Queueing Systems with Vacations Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 G. A. Afanasyev
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 308-315, August 2023. We consider a queueing system $M|G|1$ with possible vacations in server operations for principal customers (for example, if a server is leased). A cost optimization problem is solved. As control parameters, we use the probability $\alpha$ of the vacation and its duration. Under fairly general assumptions about the
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Sergey Viktorovich Nagaev (On His 90th Birthday) Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 E. B. Yarovaya
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 305-307, August 2023. This article looks back on the life of world-renowned probabilist Sergey Viktorovich Nagaev, who celebrated his 90th birthday on December 11, 2022. At present, he continues to be actively involved in various fields of probability.
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Complete and Complete Integral Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables under Sublinear Expectations Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 M. M. Xi, X. Q. Li, L. Chen, X. J. Wang
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 285-304, August 2023. We study complete and complete integration convergence for arrays of rowwise extended negatively dependent random variables under sublinear expectations. Our results generalize complete moment convergence results of [T.-C. Hu, K.-L. Wang, and A. Rosalsky, Sankhya A, 77 (2015), pp. 1--29] and [Y. Wu, M. Ordón͂ez
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Quenched Small Deviation for the Trajectory of a Random Walk with Random Environment in Time Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 Y. Lv, W. Hong
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 267-284, August 2023. We consider the small deviation probability for a random walk with random environment in time. Compared to [A. A. Mogul'skii, Theory Probab. Appl., 19 (1975), pp. 726--736], for the independent and identically distributed (i.i.d.) random walk, the rate is smaller (due to the random environment), which is specified
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Global Rate Optimality of Integral Curve Estimators in High Order Tensor Models Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 C. Banerjee, L. A. Sakhanenko, D. C. Zhu
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 250-266, August 2023. Motivated by an application in neuroimaging, we consider the problem of establishing global minimax lower bound in a high order tensor model. In particular, the methodology we describe provides the global minimax bound for the integral curve estimator proposed in [O. Carmichael and L. Sakhanenko, Linear Algebra
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Moment Asymptotics of Population Size of Particles at Vertices for a Supercritical Branching Random Walk on a Periodic Graph Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 M. V. Platonova, K. S. Ryadovkin
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 231-249, August 2023. We consider a continuous-time supercritical symmetric branching random walk on a multidimensional graph with periodic particle generation sources. A logarithmic asymptotic formula is obtained for the moments of population sizes of particles at each vertex of the graph as ${t\to\infty}$.
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Hedging Problem for Asian Call Options with Transaction Costs Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 A. A. Murzintseva, S. M. Pergamenchtchikov, E. A. Pchelintsev
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 211-230, August 2023. In this paper, we develop asymptotic Asian option hedging methods for the Black--Scholes markets with transaction costs. We first construct classical replication strategies and then, using the Leland approach, propose corresponding modifications for the financial markets with proportional transaction costs. Sufficient
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Towards Insensitivity of Nadaraya--Watson Estimators to Design Correlation Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 Yu. Yu. Linke
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 198-210, August 2023. The consistency of Nadaraya--Watson estimators in nonparametric regression is proved without using traditional conditions for dependence of design elements (regressors). A design can be either fixed and not necessarily regular, or random and not necessarily satisfying classical correlation conditions for the design
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Convergence Rates to the Arcsine Law Theory Probab. Appl. (IF 0.6) Pub Date : 2023-08-02 I. S. Borisov, E. I. Shefer
Theory of Probability &Its Applications, Volume 68, Issue 2, Page 175-197, August 2023. We study the rate of convergence of the distribution of the normalized sojourn time of a classical random walk above some nonnegative level to its limit law with unboundedly growing observation time.
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In Memory of V. A. Malyshev (04.13.1938--09.30.2022) Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 R. M. Iasnogorodski, A. A. Lykov, M.V. Melikian, S. A. Pirogov, T. S. Turova-Shmeling, A. A. Zamyatin
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 170-173, May 2023. A remembrance of the life and accomplishments of Professor Vadim Aleksandrovich Malyshev, who passed away at the age of 84 on September 30, 2022.
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Abstracts of Talks Given at the 7th International Conference on Stochastic Methods, II Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 A. N. Shiryaev, I. V. Pavlov
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 150-169, May 2023. This is the second installment of a two-part article presenting abstracts of talks given at the 7th International Conference on Stochastic Methods (ICSM-7), held June 2--9, 2022 at Divnomorskoe (near the town of Gelendzhik) at the Raduga sports and fitness center of the Don State Technical University. The conference
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Turnpikes in Finite Markov Decision Processes and Random Walk Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 A. B. Piunovskiy
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 123-149, May 2023. In this paper we revise the theory of turnpikes in discounted Markov decision processes, prove the turnpike theorem for the undiscounted model, and apply the results to the specific random walk.
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Asymptotic Relative Efficiency of the Kendall and Spearman Correlation Statistics Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 I. Pinelis
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 111-122, May 2023. A necessary and sufficient condition for Pitman's asymptotic relative efficiency of the Kendall and Spearman correlation statistics for the independence test to be $1$ is given, in terms of certain smoothness and nondegeneracy properties of the model. Corresponding easy-to-use and broadly applicable sufficient conditions
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Series Expansions of Fractional Brownian Motions and Strong Local Nondeterminism of Bifractional Brownian Motions on Balls and Spheres Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 T. Lu, C. Ma, F. Wang
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 88-110, May 2023. This paper provides series expansions for fractional Brownian motions on the unit ball and the unit sphere by means of ultraspherical polynomials and spherical harmonics. It establishes the property of strong local nondeterminism of isotropic Gaussian random fields on the unit sphere and that of fractional and bifractional
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Optimal Information Usage in Binary Sequential Hypothesis Testing Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 M. Dörpinghaus, I. Neri, É. Roldán, F. Jülicher
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 77-87, May 2023. An interesting question is whether an information theoretic interpretation can be given of optimal algorithms in sequential hypothesis testing. We prove that for the binary sequential probability ratio test of a continuous observation process, the mutual information between the observation process up to the decision
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On the Number of Trees of a Given Size in a Galton--Watson Forest in the Critical Case Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 E. V. Khvorostyanskaya
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 62-76, May 2023. We consider a critical Galton--Watson branching process starting with $N$ particles and such that the number of offsprings of each particle is distributed as $p_k=(k+1)^{-\tau}-(k+2)^{-\tau}$, $k=0,1,2,\dots$. For the corresponding Galton--Watson forest with $N$ trees and $n$ nonroot vertices, we find the limit distributions
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On the Convergence Rate in Precise Asymptotics Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 L. V. Rozovsky
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 46-61, May 2023. We study some aspects of estimation of the convergence rate in the so-called “exact asymptotics.” In particular, we obtain asymptotic expansions in powers of $\varepsilon$ of sums of the form $\sum_{n\ge 1} n^s\,\mathbf P(\xi_{\alpha}> \varepsilon n^{\delta})$, where a random variable $\xi_{\alpha}$ has a stable distribution
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Optimal Linear-Quadratic Regulator for a Stochastic System under Mutually Inverse Time Preferences in the Cost Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 E. S. Palamarchuk
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 31-45, May 2023. We investigate a long-run behavior of a linear stochastic system. It is assumed that the quadratic cost includes a time-varying function and its multiplicative inverse. Such a specification reflects the fact that time preferences used by agents to assess different types of losses evolve in opposite directions. We consider
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Probabilistic Properties of Zipf Sets and Their Maximal Intersections Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 M. A. Lifshits, I. M. Lialinov
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 16-30, May 2023. In the article, the weak and strong laws of large numbers are obtained for various characteristics of a generalized Zipf set. Based on these results, we investigate the maximal intersection size between a random Zipf set and the elements of a large base of independent random sets of the same type but, eventually, with
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On the Bounds for the Expected Maxima of Random Samples with Known Expected Maxima of Two Samples of Smaller Size Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 D. V. Ivanov
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 2-15, May 2023. Our aim in the present paper is to give a new representation of the previously known estimates and further investigate upper and lower bounds for expected maxima of $n$ independent and identically distributed (i.i.d.) standardized random variables (r.v.'s) from known expected maxima of $m$ and $p$ r.v.'s with the same
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On the 90th Birthday of I. A. Ibragimov Theory Probab. Appl. (IF 0.6) Pub Date : 2023-05-04 M. V. Khatuntseva
Theory of Probability &Its Applications, Volume 68, Issue 1, Page 1-1, May 2023. Recognition of the 90th birthday of Il'dar Abdullovich Ibragimov, world-renowned specialist in probability and mathematical statistics.
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In Memory of L. G. Afanasyeva (14.09.1937--26.08.2022) Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 Editorial Board of TPA
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 668-670, February 2023. A remembrance of the life and accomplishments of Larisa Grigor'evna Afanasyeva, who passed away on August 26, 2022.
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Abstracts of Talks Given at the 7th International Conference on Stochastic Methods, I Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 A. N. Shiryaev, I. V. Pavlov
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 652-667, February 2023. This paper presents abstracts of talks given at the 7th International Conference on Stochastic Methods (ICSM-7), held June 2--9, 2022 at Divnomorskoe (near the town of Gelendzhik) at the Raduga sports and fitness center of the Don State Technical University. The conference was chaired by A. N. Shiryaev. Participants
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On Asymptotic Expansion for Mathematical Expectation of a Renewal--Reward Process with Dependent Components and Heavy-Tailed Interarrival Times Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 R. Aliyev, V. Bayramov
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 645-651, February 2023. A renewal--reward process with dependent components and heavy-tailed interarrival times is investigated, and an asymptotic expansion as $t\to\infty$ for the expectation is derived.
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On the Maximum of a Special Random Assignment Process Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 M. A. Lifshits, A. A. Tadevosian
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 640-644, February 2023. We consider the asymptotic behavior of the expectation of the maximum for a special assignment process with constant or i.i.d. coefficients. We show how this expectation depends on the coefficients' distribution.
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Accuracy of Estimation of the Vector of Queue Lengths for Open Jackson Networks Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 E. O. Lenena
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 633-639, February 2023. The accuracy of approximation of the vector of queue lengths for an open Jackson network with regenerative input flow and unreliable servers is estimated. A theorem on the accuracy of approximation of the vector of queue lengths in open Jackson networks is put forward, i.e., an estimate for the probability of
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Partial Linear Eigenvalue Statistics for Non-Hermitian Random Matrices Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 S. O'Rourke, N. Williams
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 613-632, February 2023. For an $n \times n$ independent-entry random matrix $X_n$ with eigenvalues $\lambda_1, \dots, \lambda_n$, the seminal work of Rider and Silverstein [Ann. Probab., 34 (2006), pp. 2118--2143] asserts that the fluctuations of the linear eigenvalue statistics $\sum_{i=1}^n f(\lambda_i)$ converge to a Gaussian distribution
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Generalized Poisson--Dirichlet Distributions Based on the Dickman Subordinator Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 R. Maller, S. Shemehsavar
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 593-612, February 2023. We study exchangeable random partitions based on an underlying Dickman subordinator and the corresponding family of Poisson--Dirichlet distributions. The large sample distribution of the vector representing the block sizes and the number of blocks in a partition of $\{1,2,\dots,n\}$ is shown to be, after norming
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Uniqueness of the Inverse First-Passage Time Problem and the Shape of the Shiryaev Boundary Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 A. Klump, M. Kolb
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 570-592, February 2023. Given a distribution on the positive extended real line, the two-sided inverse first-passage time problem for Brownian motion asks for a function such that the first passage time of this function by a reflected Brownian motion has the given distribution. We combine the ideas of Ekström and Janson, which were developed
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A Guaranteed Deterministic Approach to Superhedging: The Relationship between the Deterministic and Probabilistic Problem Statements without Trading Constraints Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 S. N. Smirnov
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 548-569, February 2023. We consider a guaranteed deterministic approach to the discrete-time superreplication problem in which it is required to cover a contingent liability on a written option in all feasible scenarios. These scenarios are described by a priori given compact sets depending on the price history: at each time instant
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On Optimal Linear Regulator with Polynomial Process of External Excitations Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 E. S. Palamarchuk
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 535-547, February 2023. A linear control system over an infinite time-horizon is considered, where external excitations are defined as polynomials based on a time-varying Ornstein--Uhlenbeck process. An optimal control law with respect to long-run average type criteria is established. It is shown that the optimal control has the form
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Atypical Population Size in a Two-Type Decomposable Branching Process Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 V. A. Vatutin, E. E. D'yakonova
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 516-534, February 2023. We consider a Galton--Watson branching process with particles of two types in which particles of type one produce both particles of types one and two, and particles of type two generate offsprings of only type two. It is known that if both types are critical, then, for a process that is initiated at time $0$ by
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Stable Random Variables with Complex Stability Index, II Theory Probab. Appl. (IF 0.6) Pub Date : 2023-02-08 I. A. Alexeev
Theory of Probability &Its Applications, Volume 67, Issue 4, Page 499-515, February 2023. This paper, which is a continuation of [I. A. Alexeev, Theory Probab. Appl., 67 (2022), pp. 335--351], is concerned with $\alpha$-stable distributions with complex stability index $\alpha$. Sufficient conditions for membership in the domain of attraction of $\alpha$-stable random variables (r.v.'s) are given,