arXiv subjects

Yana Belopolskaya

Publications and source records attributed to Yana Belopolskaya.

2 recordsLinked to original sources

arXiv2020

Stationary Distributions and Convergence for M/M/1 Queues in Interactive Random Environment

A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We consider in detail two types of Markov random environments: a pure jump process and a reflected jump-diffusion. In both cases, the joint dynamics is constructed so that the stationary distribution can be explicitly found in a simple form (weighted geometric). We also derive an explicit estimate for exponential rate of convergence to the stationary distribution via coupling.

math.PR↗

arXiv2017

Stochastic models for fully coupled systems of nonlinear parabolic equations

We construct a probabilistic representation of a system of fully coupled parabolic equations arising as a model describing spatial segregation of interacting population species. We derive a closed system of stochastic equations such that its solution allows to obtain a probabilistic representation of a weak solution of the Cauchy problem for the PDE system. The corresponded stochastic system is presented in the form of a system of stochastic equations describing nonlinear Markov processes and their multiplicative functionals.

math.PR↗