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  • 1-Meixner Random Vectors
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-07-20
    Aurel I. Stan, Florin Catrina

    A definition of d-dimensional n-Meixner random vectors is given first. This definition involves the commutators of their semi-quantum operators. After that we focus on the 1-Meixner random vectors and derive a system of d partial differential equations satisfied by their Laplace transform. We provide a set of necessary conditions for this system to be integrable. We use these conditions to give a complete

    更新日期:2020-07-20
  • Self-Standardized Central Limit Theorems for Trimmed Lévy Processes
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-07-14
    David M. Mason

    We prove under general conditions that a trimmed subordinator satisfies a self-standardized central limit theorem (SSCLT). Our basic tool is a powerful distributional approximation result of Zaitsev (Probab Theory Relat Fields 74:535–566, 1987). Among other results, we obtain as special cases of our subordinator result the recent SSCLTs of Ipsen et al. (Stoch Process Appl 130:2228–2249, 2020) for trimmed

    更新日期:2020-07-15
  • Regenerativity of Viterbi Process for Pairwise Markov Models
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-07-14
    Jüri Lember, Joonas Sova

    For hidden Markov models, one of the most popular estimates of the hidden chain is the Viterbi path—the path maximising the posterior probability. We consider a more general setting, called the pairwise Markov model (PMM), where the joint process consisting of finite-state hidden process and observation process is assumed to be a Markov chain. It has been recently proven that under some conditions

    更新日期:2020-07-14
  • Hörmander’s Hypoelliptic Theorem for Nonlocal Operators
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-07-13
    Zimo Hao, Xuhui Peng, Xicheng Zhang

    In this paper we show the Hörmander hypoelliptic theorem for nonlocal operators by a purely probabilistic method: the Malliavin calculus. Roughly speaking, under general Hörmander’s Lie bracket conditions, we show the regularization effect of discontinuous Lévy noises for possibly degenerate stochastic differential equations with jumps. To treat the large jumps, we use the perturbation argument together

    更新日期:2020-07-13
  • On the Convergence of Series of Dependent Random Variables
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-06-27
    Safari Mukeru

    Given a sequence \((X_n)\) of symmetrical random variables taking values in a Hilbert space, an interesting open problem is to determine the conditions under which the series \(\sum _{n=1}^\infty X_n\) is almost surely convergent. For independent random variables, it is well known that if \(\sum _{n=1}^\infty \mathbb {E}(\Vert X_n\Vert ^2) <\infty \), then \(\sum _{n=1}^\infty X_n\) converges almost

    更新日期:2020-06-27
  • A General Version of Price’s Theorem
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-06-26
    Felix Voigtlaender

    Assume that \(X_{\Sigma } \in \mathbb {R}^{n}\) is a centered random vector following a multivariate normal distribution with positive definite covariance matrix \(\Sigma \). Let \(g : \mathbb {R}^{n} \rightarrow \mathbb {C}\) be measurable and of moderate growth, say \(|g(x)| \lesssim (1 + |x|)^{N}\). We show that the map \(\Sigma \mapsto \mathbb {E}[g(X_{\Sigma })]\) is smooth, and we derive convenient

    更新日期:2020-06-26
  • Concentration Inequalities for Bounded Functionals via Log-Sobolev-Type Inequalities
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-06-12
    Friedrich Götze, Holger Sambale, Arthur Sinulis

    In this paper, we prove multilevel concentration inequalities for bounded functionals \(f = f(X_1, \ldots , X_n)\) of random variables \(X_1, \ldots , X_n\) that are either independent or satisfy certain logarithmic Sobolev inequalities. The constants in the tail estimates depend on the operator norms of k-tensors of higher order differences of f. We provide applications for both dependent and independent

    更新日期:2020-06-12
  • Maximum Drawdown and Drawdown Duration of Spectrally Negative Lévy Processes Decomposed at Extremes
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-06-06
    Ceren Vardar-Acar, Mine Çağlar, Florin Avram

    Path decomposition is performed to characterize the law of the pre-/post-supremum, post-infimum and the intermediate processes of a spectrally negative Lévy process taken up to an independent exponential time T. As a result, mainly the distributions of the supremum of the post-infimum process and the maximum drawdown of the pre-/post-supremum, post-infimum processes and the intermediate processes are

    更新日期:2020-06-06
  • Correction to: Cylindrical Martingale Problems Associated with Lévy Generators
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-06-03
    David Criens

    In this note, we correct claims made in.

    更新日期:2020-06-03
  • On the Long-Range Dependence of Mixed Fractional Poisson Process
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-06-02
    K. K. Kataria, M. Khandakar

    In this paper, we show that the mixed fractional Poisson process (MFPP) exhibits the long-range dependence property. It is proved by establishing an asymptotic result for the covariance of inverse mixed stable subordinator. Also, it is shown that the increment process of the MFPP, namely the mixed fractional Poissonian noise, has the short-range dependence property.

    更新日期:2020-06-02
  • A Penalised Model Reproducing the Mod-Poisson Fluctuations in the Sathé–Selberg Theorem
    J. Theor. Probab. (IF 0.682) Pub Date : 2020-03-27
    Yacine Barhoumi-Andréani

    We construct a probabilistic model for the number of divisors of a random uniform integer that converges in the mod-Poisson sense to the same limiting function as its original counterpart, the one arising in the Sathé–Selberg theorem. This construction involves a conditioning and gives an alternative perspective to the usual paradigm of “hybrid product” models developed by Gonek, Hughes and Keating

    更新日期:2020-03-27
  • Self-similar Growth Fragmentations as Scaling Limits of Markov Branching Processes
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-12-17
    Benjamin Dadoun

    We provide explicit conditions, in terms of the transition kernel of its driving particle, for a Markov branching process to admit a scaling limit toward a self-similar growth fragmentation with negative index. We also derive a scaling limit for the genealogical embedding considered as a compact real tree.

    更新日期:2019-12-17
  • Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-11-25
    Benjamin Gess, Cheng Ouyang, Samy Tindel

    We consider finite-dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the corresponding solution for any fixed time \(t>0\). In addition, we provide Varadhan estimates for the asymptotic behavior of the density for small noise. The emphasis is

    更新日期:2019-11-25
  • Talagrand Inequality at Second Order and Application to Boolean Analysis
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-11-04
    Kevin Tanguy

    This note is concerned with an extension, at second order, of an inequality on the discrete cube \(C_n=\{-\,1,1\}^n\) (equipped with the uniform measure) due to Talagrand (Ann Probab 22:1576–1587, 1994). As an application, the main result of this note is a theorem in the spirit of a famous result from Kahn et al. (cf. Proceedings of 29th Annual Symposium on Foundations of Computer Science, vol 62.

    更新日期:2019-11-04
  • Bridges with Random Length: Gamma Case
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-10-26
    Mohamed Erraoui, Astrid Hilbert, Mohammed Louriki

    In this paper, we generalize the concept of gamma bridge in the sense that the length will be random, that is, the time to reach the given level is random. The main objective of this paper is to show that certain basic properties of gamma bridges with deterministic length stay true also for gamma bridges with random length. We show that the gamma bridge with random length is a pure jump process and

    更新日期:2019-10-26
  • Pinned Diffusions and Markov Bridges
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-10-23
    Florian Hildebrandt, Sylvie Rœlly

    In this article, we consider a family of real-valued diffusion processes on the time interval [0, 1] indexed by their prescribed initial value \(x \in \mathbb {R}\) and another point in space, \(y \in \mathbb {R}\). We first present an easy-to-check condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in y at time \(t=1\). Our main result then concerns the following

    更新日期:2019-10-23
  • Limit Theorems for Cylindrical Martingale Problems Associated with Lévy Generators
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-10-17
    David Criens

    We prove limit theorems for cylindrical martingale problems associated with Lévy generators. Furthermore, we give sufficient and necessary conditions for the Feller property of well-posed problems with continuous coefficients. We discuss two applications. First, we derive continuity and linear growth conditions for the existence of weak solutions to infinite-dimensional stochastic differential equations

    更新日期:2019-10-17
  • Cramér Moderate Deviation Expansion for Martingales with One-Sided Sakhanenko’s Condition and Its Applications
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-10-05
    Xiequan Fan, Ion Grama, Quansheng Liu

    We give a Cramér moderate deviation expansion for martingales with differences having finite conditional moments of order \(2+\rho , \rho \in (0,1]\), and finite one-sided conditional exponential moments. The upper bound of the range of validity and the remainder of our expansion are both optimal. Consequently, our result leads to a one-sided moderate deviation principle for martingales. Moreover,

    更新日期:2019-10-05
  • Constructive Regularization of the Random Matrix Norm
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-07-03
    Elizaveta Rebrova

    We study the structure of \(n \times n\) random matrices with centered i.i.d. entries having only two finite moments. In the recent joint work with R. Vershynin, we have shown that the operator norm of such matrix A can be reduced to the optimal order \(O(\sqrt{n})\) with high probability by zeroing out a small submatrix of A, but did not describe the structure of this “bad” submatrix nor provide a

    更新日期:2019-07-03
  • Nearly Hyperharmonic Functions are Infima of Excessive Functions
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-06-20
    Wolfhard Hansen, Ivan Netuka

    Let \(\mathfrak {X}\) be a Hunt process on a locally compact space X such that the set \(\mathcal {E}_{\mathfrak {X}}\) of its Borel measurable excessive functions separates points, every function in \(\mathcal {E}_{\mathfrak {X}}\) is the supremum of its continuous minorants in \({\mathcal {E}}_{{\mathfrak {X}}}\), and there are strictly positive continuous functions \(v,w\in {\mathcal {E}}_{{\mathfrak

    更新日期:2019-06-20
  • Moment Bounds for Large Autocovariance Matrices Under Dependence
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-06-13
    Fang Han, Yicheng Li

    The goal of this paper is to obtain expectation bounds for the deviation of large sample autocovariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent data has been well understood, much less is known in the case of dependent data. We make a step toward filling this gap and establish deviation bounds that depend

    更新日期:2019-06-13
  • A Donsker-Type Theorem for Log-Likelihood Processes
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-06-13
    Zhonggen Su, Hanchao Wang

    Let \((\Omega , \mathcal {F}, (\mathcal {F})_{t\ge 0}, P)\) be a complete stochastic basis, and X be a semimartingale with predictable compensator \((B, C, \nu )\). Consider a family of probability measures \(\mathbf {P}=( {P}^{n, \psi }, \psi \in \Psi , n\ge 1)\), where \(\Psi \) is an index set, \( {P}^{n, \psi }{\mathop {\ll }\limits ^\mathrm{loc}}{P}\), and denote the likelihood ratio process by

    更新日期:2019-06-13
  • An Integral Characterization of the Dirichlet Process
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-06-12
    Günter Last

    We give a new integral characterization of the Dirichlet process on a general phase space. To do so, we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new characterization of the Dirichlet distribution and a marked version of a classical characterization of the Poisson–Dirichlet distribution via invariance and independence properties

    更新日期:2019-06-12
  • Remarks on a Free Analogue of the Beta Prime Distribution
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-06-11
    Hiroaki Yoshida

    We introduce the free analogue of the classical beta prime distribution by the multiplicative free convolution of the free Poisson and the reciprocal of free Poisson distributions, and related free analogues of the classical F, T, and beta distributions. We show the rationales of our free analogues via the score functions and the potentials. We calculate the moments of the free beta prime distribution

    更新日期:2019-06-11
  • Borodin–Péché Fluctuations of the Free Energy in Directed Random Polymer Models
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-23
    Zsófia Talyigás, Bálint Vető

    We consider two directed polymer models in the Kardar–Parisi–Zhang (KPZ) universality class: the O’Connell–Yor semi-discrete directed polymer with boundary sources and the continuum directed random polymer with (m, n)-spiked boundary perturbations. The free energy of the continuum polymer is the Hopf–Cole solution of the KPZ equation with the corresponding (m, n)-spiked initial condition. This new

    更新日期:2019-05-23
  • Isotropic Covariance Matrix Functions on Compact Two-Point Homogeneous Spaces
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-22
    Tianshi Lu, Chunsheng Ma

    The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and sufficient conditions are derived for a symmetric and continuous matrix function to be an isotropic covariance matrix function on all compact two-point homogeneous

    更新日期:2019-05-22
  • Random Walks on Finite Quantum Groups
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-20
    Isabelle Baraquin

    In this paper, we study convergence of random walks, on finite quantum groups, arising from linear combination of irreducible characters. We bound the distance to the Haar state and determine the asymptotic behavior, i.e., the limit state if it exists. We note that the possible limits are any central idempotent state. We also look at cutoff phenomenon in the Sekine finite quantum groups.

    更新日期:2019-05-20
  • Quenched Invariance Principles for Orthomartingale-Like Sequences
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-20
    Magda Peligrad, Dalibor Volný

    In this paper, we study the central limit theorem and its functional form for random fields which are started not from their equilibrium, but rather under the measure conditioned by the past sigma field. The initial class considered is that of orthomartingales and then the result is extended to a more general class of random fields by approximating them, in some sense, with an orthomartingale. We construct

    更新日期:2019-05-20
  • Lower Bound for the Coarse Ricci Curvature of Continuous-Time Pure-Jump Processes
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-20
    Denis Villemonais

    We obtain a lower bound for the coarse Ricci curvature of continuous-time pure-jump Markov processes, with an emphasis on interacting particle systems. Applications to several models are provided, with a detailed study of the herd behavior of a simple model of interacting agents.

    更新日期:2019-05-20
  • Functional Inequalities for Feynman–Kac Semigroups
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-15
    James Thompson

    Using the tools of stochastic analysis, we prove various gradient estimates and Harnack inequalities for Feynman–Kac semigroups with possibly unbounded potentials. One of the main results is a derivative formula which can be used to characterize a lower bound on Ricci curvature using a potential.

    更新日期:2019-05-15
  • On the Long-Time Behavior of a Perturbed Conservative System with Degeneracy
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-11
    Wenqing Hu

    We consider in this work a model conservative system subject to dissipation and Gaussian-type stochastic perturbations. The original conservative system possesses a continuous set of steady states and is thus degenerate. We characterize the long-time limit of our model system as the perturbation parameter tends to zero. The degeneracy in our model system carries features found in some partial differential

    更新日期:2019-05-11
  • Stable Processes with Stationary Increments Parameterized by Metric Spaces
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-10
    Zuopeng Fu, Yizao Wang

    A new family of stable processes indexed by metric spaces with stationary increments is introduced. They are special cases of a new family of set-indexed stable processes with Chentsov representation. At the heart of the representation, a result on the so-called measure definite kernels is of independent interest. A limit theorem for set-indexed processes is also established.

    更新日期:2019-05-10
  • Scaling Limits of Random Walk Bridges Conditioned to Avoid a Finite Set
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-09
    Kôhei Uchiyama

    This paper concerns a scaling limit of a one-dimensional random walk \(S^x_n\) started from x on the integer lattice conditioned to avoid a non-empty finite set A, the random walk being assumed to be irreducible and have zero mean. Suppose the variance \(\sigma ^2\) of the increment law is finite. Given positive constants b, c and T, we consider the scaled process \(S^{b_N}_{[tN]}/\sigma \sqrt{N}\)

    更新日期:2019-05-09
  • The Distribution of Permutation Matrix Entries Under Randomized Basis
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-06
    Benjamin Tsou

    We study the distribution of entries of a random permutation matrix under a “randomized basis,” i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under certain conditions, the linear combination of entries of a random permutation matrix under a “randomized basis” converges to a sum of independent variables \(sY+Z\)

    更新日期:2019-05-06
  • On Free Regular and Bondesson Convolution Semigroups
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-05-03
    A. Kuznetsov

    Free regular convolution semigroups describe the distribution of free subordinators, while Bondesson class convolution semigroups correspond to classical subordinators with completely monotone Lévy density. We show that these two classes of convolution semigroups are in bijection with the class of complete Bernstein functions, and we establish an integral identity linking the two semigroups. We provide

    更新日期:2019-05-03
  • Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with $$ 1/4
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-04-25
    Héctor Araya, Jorge A. León, Soledad Torres

    In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter \( H \in \left( 1/4, 1/2 \right) \). Toward this end, we apply Doss–Sussmann representation of the solution and an approximation of this representation using a first-order Taylor expansion. The obtained rate of convergence is \(n^{-2H +\rho }\), for \(\rho \)

    更新日期:2019-04-25
  • Local Semicircle Law Under Fourth Moment Condition
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-04-25
    F. Götze, A. Naumov, A. Tikhomirov

    We consider a random symmetric matrix \(\mathbf{X}= [X_{jk}]_{j,k=1}^n\) with upper triangular entries being independent random variables with mean zero and unit variance. Assuming that \( \max _{jk} {{\,\mathrm{\mathbb {E}}\,}}|X_{jk}|^{4+\delta } < \infty , \delta > 0\), it was proved in Götze et al. (Bernoulli 24(3):2358–2400, 2018) that with high probability the typical distance between the Stieltjes

    更新日期:2019-04-25
  • Range and Speed of Rotor Walks on Trees
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-04-20
    Wilfried Huss, Ecaterina Sava-Huss

    We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton–Watson trees. We also show the existence of the speed for such rotor walks. More precisely, we show that on the classes of trees under consideration, even in the case when the rotor walk is recurrent, the range grows at linear speed.

    更新日期:2019-04-20
  • Gaussian Fluctuations for Linear Eigenvalue Statistics of Products of Independent iid Random Matrices
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-04-20
    Natalie Coston, Sean O’Rourke

    Consider the product \(X = X_{1}\cdots X_{m}\) of m independent \(n\times n\) iid random matrices. When m is fixed and the dimension n tends to infinity, we prove Gaussian limits for the centered linear spectral statistics of X for analytic test functions. We show that the limiting variance is universal in the sense that it does not depend on m (the number of factor matrices) or on the distribution

    更新日期:2019-04-20
  • On Hitting Time, Mixing Time and Geometric Interpretations of Metropolis–Hastings Reversiblizations
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-04-16
    Michael C. H. Choi, Lu-Jing Huang

    Given a target distribution \(\mu \) and a proposal chain with generator Q on a finite state space, in this paper, we study two types of Metropolis–Hastings (MH) generator \(M_1(Q,\mu )\) and \(M_2(Q,\mu )\) in a continuous-time setting. While \(M_1\) is the classical MH generator, we define a new generator \(M_2\) that captures the opposite movement of \(M_1\) and provide a comprehensive suite of

    更新日期:2019-04-16
  • Total Variation Approximation of Random Orthogonal Matrices by Gaussian Matrices
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-04-13
    Kathryn Stewart

    The topic of this paper is the asymptotic distribution of the entries of random orthogonal matrices distributed according to Haar measure. We examine the total variation distance between the joint distribution of the entries of \(W_n\), the \(p_n \times q_n\) upper-left block of a Haar-distributed matrix, and that of \(p_nq_n\) independent standard Gaussian random variables and show that the total

    更新日期:2019-04-13
  • Law of the First Passage Triple of a Spectrally Positive Strictly Stable Process
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-04-11
    Zhiyi Chi

    For a spectrally positive and strictly stable process with index in (1, 2), a series representation is obtained for the joint distribution of the “first passage triple” that consists of the time of first passage and the undershoot and the overshoot at first passage. The result leads to several corollaries, including (1) the joint law of the first passage triple and the pre-passage running supremum

    更新日期:2019-04-11
  • Stable Lévy Motion with Values in the Skorokhod Space: Construction and Approximation
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-03-30
    Raluca M. Balan, Becem Saidani

    In this article, we introduce an infinite-dimensional analogue of the \(\alpha \)-stable Lévy motion, defined as a Lévy process \(Z=\{Z(t)\}_{t \ge 0}\) with values in the space \({\mathbb {D}}\) of càdlàg functions on [0, 1], equipped with Skorokhod’s \(J_1\) topology. For each \(t \ge 0\), Z(t) is an \(\alpha \)-stable process with sample paths in \({\mathbb {D}}\), denoted by \(\{Z(t,s)\}_{s\in

    更新日期:2019-03-30
  • Inhomogeneous Percolation on Ladder Graphs
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-03-29
    Réka Szabó, Daniel Valesin

    We define an inhomogeneous percolation model on “ladder graphs” obtained as direct products of an arbitrary graph \(G = (V,E)\) and the set of integers \({\mathbb {Z}}\). (Vertices are thought of as having a “vertical” component indexed by an integer.) We make two natural choices for the set of edges, producing an unoriented graph \({\mathbb {G}}\) and an oriented graph \(\vec {{\mathbb {G}}}\). These

    更新日期:2019-03-29
  • Asymptotics of One-Dimensional Lévy Approximations
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-03-25
    Arno Berger, Chuang Xu

    For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic approximations relative to the classical Lévy probability metric, given any number of atoms, and allowing for additional constraints regarding locations or weights of atoms. The precise asymptotics (as the number of atoms goes to infinity) of the approximation

    更新日期:2019-03-25
  • Large Deviations for Scaled Sums of p -Adic-Valued Rotation-Symmetric Independent and Identically Distributed Random Variables
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-03-22
    Kumi Yasuda

    The law of an appropriately scaled sum of p-adic-valued, independent, identically and rotation-symmetrically distributed random variables weakly converges to a semi-stable law, if the tail probabilities of the variables satisfy some assumption. If we consider a scaled sum of such random variables with a sufficiently much higher scaling order, it accumulates to the origin, and the mass of any set not

    更新日期:2019-03-22
  • Limits for Partial Maxima of Gaussian Random Vectors
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-03-16
    James Kuelbs, Joel Zinn

    We obtain almost sure limit theorems for partial maxima of norms of a sequence of Banach-valued Gaussian random variables.

    更新日期:2019-03-16
  • Some Results on the Brownian Meander with Drift
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-03-14
    F. Iafrate, E. Orsingher

    In this paper we study the drifted Brownian meander that is a Brownian motion starting from u and subject to the condition that \( \min _{ 0\le z \le t} B(z)> v \) with \( u > v \). The limiting process for \( u \downarrow v \) is analysed, and the sufficient conditions for its construction are given. We also study the distribution of the maximum of the meander with drift and the related first-passage

    更新日期:2019-03-14
  • On Distributions Determined by Their Upward, Space–Time Wiener–Hopf Factor
    J. Theor. Probab. (IF 0.682) Pub Date : 2019-03-05
    Loïc Chaumont, Ron Doney

    According to the Wiener–Hopf factorization, the characteristic function \(\varphi \) of any probability distribution \(\mu \) on \(\mathbb {R}\) can be decomposed in a unique way as $$\begin{aligned} 1-s\varphi (t)=[1-\chi _-(s,it)][1-\chi _+(s,it)],\quad |s|\le 1,\,t\in \mathbb {R}\,, \end{aligned}$$ where \(\chi _-(e^{iu},it)\) and \(\chi _+(e^{iu},it)\) are the characteristic functions of possibly

    更新日期:2019-03-05
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