Petryna G. Asymptotic behavior of solutions of stochastic functional-differential equations

The modern development of applied mathematics and probability theory stimulates an in-depth analysis of dynamic systems whose future evolution depends on their past states. Processes characterized by delays or «memory» find wide application in biology, physics, engineering, and economics. The study is focused on investigating the asymptotic behavior of solutions of stochastic functional-differential equations with delay and on developing practical methods for approximating such systems by delay-free models. The research considers both finite-dimensional and infinite-dimensional models that take into account random perturbations and time delays. Special attention is given to the development of approaches that allow one to compare the behavior of delayed systems with the corresponding delay-free models, which significantly simplifies the analysis of the long-term dynamics of processes where the influence of previous states is critical. This approach has enabled not only the description but also the prediction of the stability and changes in the systems under consideration.