Theory of Probability &Its Applications, Volume 65, Issue 1, Page 175-178, January 2020. Obituary of outstanding mathematician Vladimir Mikhailovich Zolotarev, who passed away November 7, 2019. He is remembered as a supreme master of both modern and classical techniques of analysis who enriched the store of probability theory through his contributions of novel analytical methods and tools.

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 173-174, January 2020. An obituary of Dmitrii Mikhailovich Chibisov, the former deputy editor-in-chief of Theory of Probability and Its Applications, who passed away on November 20, 2019.

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 121-172, January 2020. This paper presents abstracts of the talks presented at The Fourth International Conference on Stochastic Methods (ICSM-4), which was held June 2--9, 2019 at Divnomorskoe (near the town of Gelendzhik) at the Raduga sports and fitness center of the Don State Technical University. Participants included many leading

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 114-120, January 2020. We consider Boolean functions $f$ defined on Boolean cube $\{-1,1\}^n$ of half-spaces, i.e., functions of the form $f(x)=\operatorname{sign}(\omega\cdot x-\theta)$. Half-space functions are often called linear threshold functions. We assume that the Boolean cube $\{-1,1\}^n$ is equipped with a uniform measure.

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 111-113, January 2020. We study the form of excursions of a Gaussian stationary process intersecting a high level $u$. We show that the trajectories fluctuate in this case in a narrow tube around the expected motion. We also find an upper bound for the probability that the trajectory intersects the boundary of this tube as $u$ goes off

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 102-110, January 2020. We consider a stationary linear $\operatorname{AR}(p)$-model with observations subject to gross errors (outliers). The autoregression parameters and the distribution of innovations are unknown. Based on the residuals from the parameter estimators, we construct an analogue of an empirical distribution function and

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 82-101, January 2020. We derive sufficient conditions for the differentiability of all orders for the flow of stochastic differential equations with jumps and prove related $L^p$-integrability results for all orders. Our results extend similar results obtained by H. Kunita [Stochastic differential equations based on Lévy processes and

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 62-81, January 2020. We explore the asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 49-61, January 2020. We consider the problem of constructing guarantee procedures of statistical inference with fixed minimal observation number $n^*$ for discrimination of two hypotheses $H_0\colon\theta\in[\theta_1,\theta_2]$ and $H_1\colon\theta\notin[\theta_1,\theta_2]$ with a one-dimensional parameter $\theta$ under the so-called

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 32-48, January 2020. Sample statistics of samples from a fractional Brownian motion with Hurst exponent $H$, and in particular, autocovariance statistics, are considered. Two statistics characterizing the covariate dependence between the increments of this process are studied; in particular, their asymptotic properties and the limit

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 17-31, January 2020. We examine the asymptotic behavior of integral quadratic functionals defined on time-varying Ornstein--Uhlenbeck processes. We find an upper function that majorizes with probability $1$ the deviation of the integral from its expected value as time increases. The results obtained are applied to evaluate the control

Theory of Probability &Its Applications, Volume 65, Issue 1, Page 1-16, January 2020. We consider statistics of the form $T =\sum_{j=1}^n \xi_{j} f_{j}+ \mathcal R $, where $\xi_j, f_j$, $j=1, \dots, n$, and $\mathcal R$ are $\mathfrak M$-measurable random variables for some $\sigma$-algebra $ \mathfrak M$. Assume that there exist $\sigma$-algebras $\mathfrak M^{(1)}, \dots, \mathfrak M^{(n)}$, $ \mathfrak

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 656-656, January 2020. A remembrance of the life and accomplishments of Vadim Rolandovich Fatalov, who passed away on June 4, 2019.

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 646-655, January 2020. In this paper a two-dimensional Brownian motion (modeling the endowment of two companies), absorbed at the boundary of the positive quadrant, with controlled drift, is considered. We allow that both drifts add up to the maximal value of one. Our target is to choose the strategy in a way s.t. the expected value

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 636-645, January 2020. When collecting samples, sometimes failures of observations occur and consequently missing data. This can have an impact on the analysis and subsequent inference, especially if the study focuses on the extreme values where the data is more scarce. In this work, we analyze the effect of different types of failures

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 631-635, January 2020. It is known that the values of functions that depend on a large number of similar variables are almost constant from the point of view of an observer evaluating their values at random points of the domains of their definition (the “nonlinear law of large numbers''). We show that, under certain normalization conditions

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 615-630, January 2020. This paper describes Fatou's lemma for a sequence of measures converging weakly to a finite measure and for a sequence of functions whose negative parts are uniformly integrable with respect to these measures. The paper also provides new formulations of uniform Fatou's lemma, uniform Lebesgue's convergence theorem

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 595-614, January 2020. Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 579-594, January 2020. We study the relationship between the well-known Carleman's condition guaranteeing that a probability distribution is uniquely determined by its moments, and a recent, easily checkable condition on the rate of growth of the moments. We use asymptotic methods in the theory of integrals and involve properties of

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 564-578, January 2020. The remainder term in the integro-local version of the multidimensional central limit theorem for a sum of independent random vectors is studied with due account of asymptotic expansions. It is assumed that the distribution of this sum can be absolutely continuous and/or lattice in some coordinates.

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 553-563, January 2020. We consider a problem of utility maximization for multiperiod asset trading in a general model of connected financial markets represented by a graph. The main result of the paper is a theorem providing conditions for the existence of a system of supporting prices in this model. Using the general result, a specific

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 535-552, January 2020. A conditional limit theorem is proved describing the distribution of the population size in the initial evolution stage of a weakly subcritical branching process in a random environment given its survival for a long time.

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 513-534, January 2020. We consider a supercritical catalytic branching random walk (CBRW) with finite number of catalysts on a multidimensional lattice $\mathbb{Z}^d$, $d\in{N}$. The behavior of a cloud of particles in space and time is studied. When estimating the rate of the population propagation for the front of a multidimensional

Theory of Probability &Its Applications, Volume 64, Issue 4, Page 499-512, January 2020. We find the asymptotics for the logarithm of the Laplace transform of the distribution of a compound renewal process as time increases unboundedly. It is assumed that the elements of the governing sequences of the renewal process satisfy Cramér's moment condition. Representations for the deviation rate function