**About the Editors**

**Alexander Zeifman** Professor, Head of Department of Applied Mathematics, Vologda State University, Vologda, Russia; Senior Researcher, Institute of Informatics Problems, Federal Research Center "Computer Sciences and Control" of the Russian Academy of Sciences, Russia; Chief Researcher, Vologda Research Center of the Russian Academy of Sciences, Russia.

Graduate of Vologda State Pedagogical Institute, 1976. Candidate of Science in Physics and Mathematics (Ph.D.), 1981. Doctor of Science in Physics and Mathematics (1994, Institute of Control Sciences, Russian Academy of Sciences). Main research interests: stochastic models, continuous-time Markov chains, bounds on the rate of convergence, perturbation bounds, queueing models, biological models, and queueing theory.

**Victor Korolev** Professor, Head of Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia; Leading researcher, Institute of Informatics Problems, Federal Research Center "Computer Sciences and Control" of the Russian Academy of Sciences, Moscow, Russia; Professor, Hangzhou Dianzi University, Hangzhou, China.

Graduate of Faculty of Computational Mathematics, Lomonosov Moscow State University, 1977. Candidate of Science in Physics and Mathematics (Ph.D.), 1981. Doctor of Science in Physics and Mathematics (1994, Lomonosov Moscow State University).

Main research interests: limit theorems of probability theory and their applications in distribution theory, statistics, risk theory, and reliability theory; probability models of real processes in physics, meteorology, financial mathematics, and other fields.

**Alexander Sipin** Professor at the Department of Applied Mathematics, Vologda State University, Institute of Mathematics, Natural and Computer Sciences, Russia.

Graduate of Faculty of Mathematics and Mechanics, Leningrad State University, now St. Petersburg State University, Russia in 1975. Candidate of Science in Physics and Mathematics (Ph.D.), 1979. Doctor of Science in Physics and Mathematics (2016, St. Petersburg State University, Russia).

Research interests: Monte Carlo and quasi-Monte Carlo methods, Markov chains, and meshless numerical methods for solving boundary value problems.

#### **Preface to "Stability Problems for Stochastic Models"**

The aim of this Special Issue of *Mathematics* is to commemorate the outstanding Russian mathematician Vladimir Zolotarev whose 90th birthday will be celebrated on February 27th, 2021.

Through his mathematical maturation, Zolotarev took much from distinguished mathematicians E. B. Dynkin and A.N. Kolmogorov, who were his direct teachers during his studies at Lomonosov Moscow State University, in addition to B.V. Gnedenko and Yu. V. Linnik during his graduate studies. In 1958, he defended his candidate (Ph.D.) thesis "Analytic Properties of Infinitely Divisible Distribution Laws" prepared under the supervision of academician Andrey Kolmogorov. In 1966, Vladimir Zolotarev defended his second thesis "Distribution of Sums of Independent Random Variables and Stochastic Processes with Independent Increments" and obtained the degree of Doctor of Sciences. One of his main interests was study of the properties of stable distributions. Zolotarev extended the concept of stable law to the schemes of maximum and multiplication of random variables. Zolotarev's studies on stable laws were summarized in the book "One-Dimensional Stable Distributions" published in 1983, which was soon translated into English (1985) and quickly gained widespread recognition. As this book saw the light, concepts such as Zolotarev's theorem, Zolotarev's formula, and the Zolotarev transformation became quite conventional. Contemporaneously with the study of stable laws, Zolotarev began to work in the field of limit theorems for sums of independent random variables. He made a substantial contribution to the so-called nonclassical theory of summation. The cornerstone of this scheme was the break of the habitual approach, in which an individual summand does not have an effect on the form of the limit distribution (in nonclassical summation theory, an individual summand may play a prominent role). It is fair to say that Vladimir Zolotarev is one of the fathers of this direction in probability theory. He generalized the results of his predecessors, P. Levy and Yu. V. Linnik who, on the heuristic level, pointed out the possibility ´ of a new approach to limit theorems for sums of independent random variables. The key point of this approach is that limit theorems of probability theory are treated as special stability theorems. Zolotarev created the theoretical foundation of the key method used within this approach, the theory of probability metrics. This approach assumes that statements establishing convergence must be accompanied by statements establishing the convergence rate. Zolotarev called the conditions of convergence that simultaneously serve as convergence rate estimates "natural", In the 1970s, the annual International Seminar on Stability Problems for Stochastic Models were launched, with wide participation of mathematicians from many countries. Today, this seminar is internationally recognized for the originality and relevance of the considered problems and presented results. The seminar formed and developed a breakthrough approach to limit theorems of probability theory as stability theorems. Below is the complete list of the sessions of the International Seminar on Stability Problems for Stochastic Models:


IX: 13–19 May 1985, Varna, Bulgaria X: October 1986, Kuybyshev (now Samara), USSR XI: 4–11 October 1987, Sukhumi, Abkhasian ASSR XII: October 1988, Kharkov, Ukrainian SSR XIII: October 1989, Kirillov, Vologda Region, USSR XIV: 27 January–2 February 1991, Suzdal, USSR XV: 1–6 June 1992, Perm, Russia XVI: 29 August–3 September 1994, Eger, Hungary XVII: 19–26 June 1995, Kazan', Russia XVIII: 26 January–1 February 1997, Hajduszoboszl ´ o, Hungary ´ XIX: 6–12 September 1998, Vologda, Russia XX: 5–11 September 1999, Nałeczow, Poland ´ XXI: 28 January–3 February 2001, Eger, Hungary XXII: 25–31 May 2002, Varna, Bulgaria XXIII: 12–17 May 2003, Pamplona, Spain XXIV: 10–17 September 2004, Majori (Jurmala), Latvia XXV: 20–24 September 2005, Maiori (Salerno), Italy XXVI: 27 August–2 September 2006, Sovata-Bai, Romania XXVII: 22–26 October 2007, Nahariya, Israel XXVIII: 31 May–5 June 2009, Zakopane, Poland XXIX: 10–16 October 2011, Svetlogorsk, Russia XXX: 24–30 September 2012, Svetlogorsk, Russia XXXI: 23–27 April 2013, Moscow, Russia XXXII: 15–21 June 2014, Trondheim, Norway XXXIII: 13–18 June 2016, Svetlogorsk, Russia XXXIV: 24–28 August 2017, Debrecen, Hungary XXXV: 24–28 September 2018, Perm, Russia XXXVI: 22–26 June 2020, Petrozavodsk, Russia (online session),Russia (offline session).

Devoting his heart and soul to science, he had always demanded the same from his colleagues and numerous students. Vladimir Zolotarev had to spend the last years of his life away from Russia in California (USA), where the local equable climate helped him overcome the consequences of a stroke suffered in 1995. On November 7, 2019, the outstanding mathematician Vladimir Mikhailovich Zolotarev passed away.

The present Special Issue contains a collection of new papers by the colleagues and followers of Vladimir Zolotarev, who were participants in sessions of the International Seminar on Stability Problems for Stochastic Models.

> **Alexander Zeifman, Victor Korolev, Alexander Sipin** *Editors*

 21–25 June 2021,

Petrozavodsk,
