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.

Upcoming reports

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.

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

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