Khasminskii’s Theorem for the Kolmogorov Equation with Partially Degenerate Diffusion Matrix

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030155

S. V. Shaposhnikov, D. V. Shatilovich

引用次数: 0

Abstract

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

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具有部分退化扩散矩阵的柯尔莫哥洛夫方程的哈斯明斯基定理

摘要研究了具有部分退化扩散矩阵和不连续漂移系数的静态 Kolmogorov 方程。获得了概率解存在的充分条件。举例说明了这些条件的尖锐性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.