Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:I. A. Alexeev Pages: 335 - 351 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 335-351, November 2022. The present paper is the first part of a work on stable distributions with a complex stability index. We construct complex-valued random variables (r.v.'s) satisfying the usual stability condition but for a complex parameter $\alpha$ such that $ \alpha-1 Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T990976 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:D. M. Balashova Pages: 352 - 362 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 352-362, November 2022. We consider a time-continuous symmetric branching random walk over a multidimensional lattice with particles of several types and a Markov branching process at each point of the lattice. It is assumed that initially at each lattice point there is one particle of each type, and any particle can produce an arbitrary number of descendants of each type in the process of branching. For the transient random walk and the critical branching process, the effect of spatial clusterization of the population particles is studied. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T990988 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:L. V. Rozovsky Pages: 363 - 374 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 363-374, November 2022. Given a sum of a finite number of independent random variables (r.v.'s), the asymptotic behavior of its distributions and densities at infinity is investigated in the case when the densities or tails of these distributions decrease faster than the densities or tails of gamma distributions. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T99099X Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:P. A. Yaskov Pages: 375 - 388 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 375-388, November 2022. For sample covariance matrices associated with random vectors having graphdependent entries and a number of dimensions growing with the sample size, we derive sharp conditions for the limiting spectrum of the matrices to have the same form as in the case of Gaussian data with similar covariance structure. Our results are tight. In particular, they give necessary and sufficient conditions for the Marchenko--Pastur theorem for sample covariance matrices associated with random vectors having $m$-dependent orthonormal elements when $m=o(n)$. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991003 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:M. Biret, M. Broniatowski, Z. Cao Pages: 389 - 414 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 389-414, November 2022. We explore some properties of the conditional distribution of an independently and identically distributed (i.i.d.) sample under large exceedances of its sum. Thresholds for the asymptotic independence of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension of Broniatowski and Cao [Extremes, 17 (2014), pp. 305--336]. Tools include a new Edgeworth expansion adapted to specific triangular arrays, where the rows are generated by tilted distribution with diverging parameters, and some Abelian type results. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991015 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:C. Lu, W. Yu, R. L. Ji, H. L. Zhou, X. J. Wang Pages: 415 - 433 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 415-433, November 2022. Recently, Wang and Hu [Theory Probab. Appl., 63 (2019), pp. 479--499] established the Berry--Esseen bounds for $\rho$-mixing random variables (r.v.'s) with the rate of normal approximation $O(n^{-1/6}\log n)$ by using the martingale method. In this paper, we establish some general results on the rates of normal approximation, which include the corresponding ones of Wang and Hu. The rate can be as high as $O(n^{-1/5})$ or $O(n^{-1/4}\log^{1/2} n)$ under some suitable conditions. As applications, we obtain the Berry--Esseen bounds of sample quantiles based on $\rho$-mixing random samples. Finally, we also present some numerical simulations to demonstrate finite sample performances of the theoretical result. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991027 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:T. C. Son, L. V. Dung, D. T. Dat, T. T. Trang Pages: 434 - 451 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 434-451, November 2022. The aim of this paper is to apply the theory of regularly varying functions for studying Marcinkiewicz weak and strong laws of large numbers for the weighted sum $S_n=\sum_{j=1}^{m_n}c_{nj}X_j$, where $(X_n;\, n\geq 1)$ is a sequence of dependent random vectors in Hilbert spaces, and $(c_{nj})$ is an array of real numbers. Moreover, these results are applied to obtain some results on the convergence of multivariate Pareto--Zipf distributions and multivariate log-gamma distributions. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991039 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:J. Toofanpour, M. Javanian, R. Imany-Nabiyyi Pages: 452 - 464 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 452-464, November 2022. Protected nodes, i.e., nodes with distance at least 2 to each leaf, have been studied in various classes of random rooted trees. In this short note, we investigate the protected node profile, i.e., the number of protected nodes with the same distance from the root in random recursive trees. Here, when the limit ratio of the level and logarithm of tree size is zero, we present the asymptotic expectations, variances, and covariance of the protected node profile and the nonprotected node profile in random recursive trees. We also show that protected node and nonprotected node profiles have a bivariate normal limiting distribution via the joint characteristic function and singularity analysis. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991040 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:G. A. Afanasyev Pages: 465 - 472 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 465-472, November 2022. Single-channel systems where service vacation is triggered when the system is free from customers are studied. Vacations in service can mean either a complete shutdown of the server or a transition to a different regime. If, during a vacation, the number of customers in the system reaches a certain fixed threshold, the vacation terminates and the unit resumes standard operations. A delay begins if the system is free from customers after a vacation; the delay interrupts at the moment of arrival of the first customer. Then a new vacation begins if no customers have arrived. The input of the queue outside vacations is a Poisson flow, and the remaining variables, which control the performance of the system (the service time, the durations of vacations and delays) have arbitrary distributions. A stationary distribution for the number of customers in the system is determined under the assumption that the process controlling the number of customers in the system during the vacation and the planned duration of the vacation are independent. We also study the asymptotic behavior for the number of completed vacations. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991052 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:Sh. K. Formanov Pages: 473 - 477 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 473-477, November 2022. We give an analytic proof of Sakhanenko's theorem on the strong law of large numbers. Our arguments are based on the method of characteristic functions: under the Lindeberg-type condition, the expectation of the absolute value of the sum of independent random variables (r.v.'s) tends to zero. In our proof, we represent the expectation of the absolute value of an r.v. in terms of the corresponding characteristic function. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991064 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:S. Mousavinasr, C. R. Gonçalves, C. C. Y. Dorea Pages: 478 - 484 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 478-484, November 2022. We explore the Mallows distance convergence to characterize the domain of attraction for extreme value distributions. Under mild assumptions we derive the necessary and sufficient conditions. In addition to the i.i.d. case, our results apply to regenerative processes. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991076 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:I. Pinelis Pages: 485 - 493 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 485-493, November 2022. Exact upper and lower bounds on the ratio $\operatorname{\mathbf{E}}w(\mathbf{X}-\mathbf{v})/\operatorname{\mathbf{E}}w(\mathbf{X})$ for a centered Gaussian random vector $\mathbf{X}$ in $\mathbf{R}^n$ are obtained, as well as bounds on the rate of change of $\operatorname{\mathbf{E}}w(\mathbf{X}-t\mathbf{v})$ in $t$, where $w\colon\mathbf{R}^n\to[0,\infty)$ is any even unimodal function and $\mathbf{v}$ is any vector in $\mathbf{R}^n$. As a corollary of such results, exact upper and lower bounds on the power function of statistical tests for the mean of a multivariate normal distribution are given. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991088 Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:E. B. Yarovaya Pages: 494 - 497 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 494-497, November 2022. This paper presents summaries of talks given during the 2022 spring term of the General Seminar of the Department of Probability, Moscow State University. The seminar was held under the direction of A. N. Kolmogorov and B. V. Gnedenko. Current information about the seminar is available at http://new.math.msu.su/department/probab/seminar.html. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T99109X Issue No:Vol. 67, No. 3 (2022)

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:E. B. Yarovaya Pages: 498 - 498 Abstract: Theory of Probability & Its Applications, Volume 67, Issue 3, Page 498-498, November 2022. This letter presents a correction to the paper [S. V. Nagaev, An alternative method of the proof of the ergodic theorem for general Markov chains, Theory Probab. Appl., 66 (2021), pp. 364--375]. Citation: Theory of Probability & Its Applications PubDate: 2022-11-07T08:00:00Z DOI: 10.1137/S0040585X97T991106 Issue No:Vol. 67, No. 3 (2022)