ASU Researchers Showcase Breakthroughs in the Stability Analysis of Stochastic Differential Equations at International Conference

Photo: Academician Shiryaev A.N. (right) and Professor Shumafov M.M. discuss Stratonovich's approach in the theory of stochastic differential equations

Magomet Shumafov, Head of the Department of Mathematical Analysis and Methods of Teaching Mathematics, and Vyacheslav Tlyachev, Associate Professor in the Department of Theoretical Physics, presented a research paper at the 11th International Conference on Stochastic Methods, held from May 31 to June 6 in Divnomorskoye. The paper focused on the results of studies investigating the overall stability of solutions to two-dimensional nonlinear systems of differential equations perturbed by a stochastic process—specifically, Gaussian "white noise." These systems serve as mathematical models for numerous real-world phenomena subject to random disturbances. The study examined systems of stochastic differential equations (SDEs) in Stratonovich form as the mathematical framework. This approach garnered particular interest from Albert Shiryaev.

Academician of the Russian Academy of Sciences (RAS), Chairman of the Conference Program and Organizing Committee . He noted the correctness of using SDEs in the Stratonovich form when modeling certain physical processes, as opposed to SDEs in the Ito form. Furthermore, on one of the conference days, Professor Magomet Shumafov chaired the plenary and breakout sessions. The 11th International Conference on Stochastic Methods traditionally brings together leading scientists, mathematicians, and developers interested in the intersection and development of stochastic methods and artificial intelligence technologies. The conference discusses current issues in stochastic analysis, its applications in machine learning, Bayesian methods, and stochastic optimization of neural networks. The conference is organized by the Steklov Mathematical Institute of the Russian Academy of Sciences (including the Steklov Mathematical Center of the Steklov Institute of Mathematics), Moscow State University (MSU), the Steklov Institute of Mathematics, Mechanics, and Computer Science, and the Steklov Institute of Mathematics, Mechanics, and Computer Science. The conference participants included the I. I. Vorovich Southern Federal University, the Regional Scientific and Educational Mathematical Center of Southern Federal University (RSEMC SFedU), Don State Technical University (DSTU), the National Committee of the Bernoulli Society on Mathematical Statistics, Probability Theory, Combinatorics, and their Applications, the AIRI Institute, and StroyKontrol LLC. Papers from the conference proceedings will be published in the journal "Probability Theory and Its Applications" and the English version of the journal "Theory of Probability and its Applications ," founded by the Steklov Mathematical Institute of the Russian Academy of Sciences. The official website of the conference is http://www.intconfstochmet.ru/