S. V. Shaposhnikov, D. V. Shatilovich, “Khas'minskii's Theorem for the Kolmogorov Equation with Partially Singular Diffusion Matrix”, Mat. Zametki, 2024, Volume 115, Issue 3,Pages <nobr>466

Khas'minskii's Theorem for the Kolmogorov Equation with Partially Singular Diffusion Matrix

S. V. Shaposhnikov, D. V. Shatilovich

Lomonosov Moscow State University

Abstract: The stationary Kolmogorov equation with partially singular diffusion matrix and discontinuous drift coefficient is studied. Sufficient conditions for the existence of a probabilistic solution are obtained. Examples demonstrating the sharpness of these conditions are given.

Keywords: Kolmogorov equation, invariant measure of a diffusion process, Lyapunov function.

UDC: 519.217.4+517.956.226

MSC: 35A01

Received: 08.07.2023

DOI: 10.4213/mzm14100