UNITED SEMINAR OF THE DEPARTMENT OF PROBABILITY THEORY OF LOMONOSOV MOSCOW STATE UNIVERSITY
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This is the page of the United Seminar of the Department of Probability Theory of the Faculty of Mechanics and Mathematics of Moscow State University. The permanent website of the seminar is here. The seminar is a continuation of the research seminar of the Department of Probability Theory under the leadership of A.N. Kolmogorov and B.V. Gnedenko.
The seminar is held online every Wednesday from 16:45 to 17:45 Moscow time.
Permanent link to the Zoom room: http://bit.ly/3HY8K6d
Room ID: 844 6792 3144 Access code: 697663
Head of the seminar: academician of the RAS, professor Albert N. Shiryaev
Coordinator of the seminar in fall 2025: professor Elena B. Yarovaya
Secretary of the seminar in fall 2025: Oleg E. Ivlev
To subscribe to the seminar newsletter or submit a talk, click "Subscribe or submit" at the top of the page.
We recommend you to study the network of seminars at this link, which were brought together by our colleagues from the Mathematical Center of the Southern Federal University.
The list of reports from 2020 and previous years can be viewed at this link.
The list of reports from 2021-2025 can be in the corresponding sections of this page.
We recommend you to study the network of seminars at this link, which were brought together by our colleagues from the Mathematical Center of the Southern Federal University.
The list of reports from 2020 and previous years can be viewed at this link.
The list of reports from 2021-2025 can be in the corresponding sections of this page.
Upcoming reports
Upcoming reports
December 3, 16:45 msk
Andrey Zamyatin, Lomonosov MSU, Russia
On the Hitting Point Distribution for Random Walks in Bounded Domains
The report examines the classical problem of the hitting point distribution for a random walk entering a set within a two-dimensional lattice strip. The limit of this distribution is investigated as the starting point of the walk is moved far from the boundary. In the second part of the report, the obtained results are used to calculate the rate of particle accumulation on the boundary and in the problem of the growth rate of a cluster formed by the accumulated particles.
Past reports
Past reports
November 26, 16:45 msk
Egor Illarionov, Lomonosov MSU, Russia
Machine learning in mathematics and mathematics in machine learning
The development of mathematical models and methods leads to improvement of machine learning models, one of the recent achievements of which is the formation of a chain of reasoning when deriving an answer. In the first part of the presentation, we consider examples of how modern machine learning models form a chain of reasoning and solve mathematical problems, in particular in probability theory. In the second part of the presentation, using some text recognition tasks in images as an example, we consider the mathematical models and constructions behind machine learning models and what problems arise that are of interest for further research.
The recording: YouTube
November 19, 16:45 msk
Michael Boldin, Lomonosov MSU, Russia
On Kolmogorov's and Pearson's type tests in autoregression
In the first part we consider a stationary AR(p) model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical distribution function is defined and the tests of Kolmogorov's and ω^2 type are constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of these tests under local alternatives. In the second part we consider AR(p) model with observations subject to gross errors (outliers). The distribution of outliers is unknown and arbitrary, their intensity is γn^{-1/2} with an unknown γ, n is the sample size. We test the hypothesis for normality of innovations. Our test is the special symmetrized Pearson's type test. We find the power of this test under local alternatives. We establish qualitative robustness of this test in terms of uniform equicontinuity of the limiting power.
The recording: YouTube
November 12, 16:45 msk
Elena Yarovaya (jointly with A.Gusarov and E.Filichkina), Lomonosov MSU, Russia
Probabilistic methods and models in the theory of branching random walks
Branching random walks (BRWs) are a branch of the theory of stochastic processes that studies the behavior of systems whose elements can reproduce, die, and move through space. The fundamental basis for analytical methods for studying stochastic processes was largely laid by the founder of the Department of Probability Theory, A.N. Kolmogorov. Contemporary areas of research into BRWs include the study of the spatial structure of continuous-time BRWs with the underlying random walk on a multidimensional lattice: with different spatial dynamics (Rytova and Yarovaya, 2016); in non homogeneous (Yarovaya, 2007) and homogeneous (Makarova et al., 2022) branching environments; in random environments (Molchanov, 1994); with fixed spatial variables; with joint growth of spatial coordinates and time (Molchanov and Yarovaya, 2012). To study the time-limit behavior of BRWs, we use spectral (Yarovaya, 2024) and martingale methods (Smorodina and Yarovaya, 2023). One of the founders of this area of stochastic analysis is the head of the Department of Probability Theory A.N. Shiryaev (see the monograph "Brownian Motion and Wiener Measure", 2025). In our talk particular attention is given to "exactly solvable" models of BRWs, in which the random walk is defined by a difference Laplacian. This model has numerous applications in statistical physics (Zel'dovich et al., 1988), and its research remains relevant. For a BRW with one source of branching under various assumptions on the structure of the absorbing medium, in particular, when particle can die at every lattice point, a condition was obtained that guarantees exponential growth of the particle population at every lattice point (Filichkina and Yarovaya, 2023). Based on these results, new limit theorems were proved.
The recording: YouTube
November 5, 16:45 msk
Dmitry Shabanov, Lomonosov MSU, Russia
Extremal probabilistic problems for weighted graphs
The talk will be devoted to extreme problems of probabilistic combinatorics related to weighted graphs. Briefly, this class of problems can be described as follows: we assign positive random weights to elements of a certain finite set, we choose some subsets and the goal is to find a chosen subset with the minimum total weight of elements. One of the most well-known problems of the described type is concerned with finding the minimum weight of a spanning tree in a complete graph, provided that the weights of the edges are independent and equally distributed. The famous result of A. Frieze shows that under natural assumptions on the distribution of weights, the average value of the desired random variable converges to a zeta function of 3. In the talk, we discuss the connection of this problem with the classical results of random graph theory, and also present its generalization related to the search for the minimum total weight of k spanning trees.
The recording: YouTube
October 29, 16:45 msk
Gennady Falin, Lomonosov MSU, Russia
Stochastic Models of Queueing Systems with Repeated Demands
Queueing systems with repeated demands are characterized by the following feature: a demand that cannot receive full service (due to lack of available servers, balking, impatience, servers failure, etc.) leaves the service area, but after some random time is repeated until the required service is provided, or after several unsuccessful attempts the demand decides to abandon further attempts and leaves the system without service. From the mathematical point of view the problem consists in analysis of specific stochastic processes, usually random works on a multidimensional integer lattice. We give a short literature review and discuss in a few words some examples of such models.
The recording: YouTube
October 22, 16:45 msk
Alexаnder Condratenko, Lomonosov MSU, Russia
On the behavior of the fractional part of convolutions of random variables
The classical limit theorems of probability theory, the law of large numbers and the central limit theorem, speak of the convergence of convolutions of random variables in the corresponding normalizations. The convolution operation inherits the properties of absolute continuity of the term and absolute integrability of its characteristic function. However, in the CLT normalization, standard normality is not inherited. Also, the degeneracy is not inherited in the LLN normalization. The report will talk about the heritability of uniformity in the fractional part of a convolution in various cases and the convergence of the fractional part of convolutions to a uniform random variable in the integer case.
The recording: YouTube
October 15, 16:45 msk
Alexey Lebedev, Anna Goldaeva, Lomonosov MSU, Russia
Modern approaches to compexification of max-stable distributions
By analogy with the generalization of stable distributions to the domain of complex stability indices α using the representation by a stochastic integral over a Poisson random measure (I.A.Alekseev, 2021, 2022), complexification of the max-stable Frechet distribution is performed (A.V.Lebedev, 2023). The result is max-semistable distribution on the first quarter of the complex plane. Estimates are derived for marginal distribution functions. The second approach uses random angles (A.A.Goldaeva, A.V.Lebedev, 2025). Marginal distributions are found for the real and imaginary components, and the dependence is studied using copulas and other characteristics. A limit theorem is proved.
The recording: YouTube
October 8, 16:45 msk
Alexander Veretennikov, Lomonosov MSU, Russia
Stochastic differential equations: a review, the role of the Department, new results
In the beginning, a short review of the SDE theory will be offered, with the highlight of contributions in various directions of the whole area, specifically due to the Department members and their disciples. In particular, some advances in the area by the Department students under the supervision of the speaker will be briefly presented. Then a new case of existence and pathwise uniqueness of a strong solution discovered recently and studied jointly with Anastasiya Lyappieva will be presented in more details. The setting is like in the well-known Yamada and Watanabe multidimensional theorem about pathwise uniqueness (DOI: 10.1215/kjm/1250523691), where the diffusion matrix is diagonal with elements depending only on the corresponding coordinates, with the following variations. (1) the SDE in R^d is homogeneous, that is, the coefficients do not depend on time; (2) unlike in Yamada and Watanabe's paper, the diffusion matrix is assumed to be uniformly non-degenerate; (3) the drift b has a form b^i(x) = b^i_0(x^i) + b^i_1(x), 1≤i≤d, and the regularity conditions on b_1 and σ are like in Yamada and Watanabe's case; (4) all coefficients are bounded, including b_0 and b_1, and the functions b^i_0 are just Borel measurable. Under such conditions, the SDE has a pathwise unique strong solution. The paper is under preparation.
The recording: YouTube
October 1, 16:45 msk
Ekaterina Bulinskaya, Lomonosov MSU, Russia
Risk networks
Risk management (or decision making under uncertainty) is important in applications of Probability Theory such as insurance, finance, queueing, reliability, inventory control, telecommunications, population dynamics, biology, medicine and others. The first step in such investigations is to choose an appropriate model. The most popular ones are input-output models. For their description, it is necessary to know a collection (T,Z,Y,U,Ψ,𝓛), that is, a planning horizon, input, output and control processes, a functional describing the system structure and working mode, as well as, an objective function evaluating the system performance quality. Then the optimal (asymptotically optimal or ε-optimal) control is found, system's stability is established and limit theorems are proved. For illustration we consider risk networks with investment and reinsurance arising in insurance industry.
The recording: YouTube
September 24, 16:45 msk
Alexander Bulinski, Lomonosov MSU, Russia
Delta Method and its Applications
The Delta method has a long history going back to the research of the 18th century. Such famous scientists as C.F.Gauss, C.E.Spearman, K.J.Holzinger, S.G.Wright, J.L.Doob, R.E.Dorfman, C.H.Cramer, C.R.Rao, D.A.Pierce and other contributed to its development. A modern treatment of this method is explained. As an illustration, it is shown how one can construct approximate confidence intervals for an unknown parameter p in the Bernoulli scheme. At the same time, a comparison of various methods for solving this problem is provided. Moreover, new results from the article by A.Bulinski and S.Wang (Sankya A: The Indian Journal of Statistics, July, 2025, p. 1-26) related to statistical estimation of the conditional interaction information by means of Delta method are presented.
The recording: YouTube
September 17, 16:45 msk
Albert Shiryaev
N.Kordzakia, A.Novikov, A.Shiryaev. On parameter estimation of diffusion processes by maximum likelihood method
The recording: YouTube
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