任意时刻麦金-弗拉索夫随机微分方程解的稳定性、唯一性和存在性

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2024-08-19 DOI:10.1007/s10959-024-01344-2

Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske

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引用次数: 0

摘要

我们推导了具有随机系数和多维布朗运动驱动的麦金-弗拉索夫方程的稳定性和路径唯一性。我们的分析重点是非 Lipschitz 连续漂移，并包括与之相关的随机 Itô 过程的矩估计。对于确定性系数，即使漂移不具有仿射增长性，我们也能提供唯一的强解。我们所发展的理论建立在伊托公式的基础上，并通过明确的Lyapunov指数为\(p\ge 2\) 引出了pth矩和路径指数稳定性。

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Stability, Uniqueness and Existence of Solutions to McKean–Vlasov Stochastic Differential Equations in Arbitrary Moments

We deduce stability and pathwise uniqueness for a McKean–Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz continuous drift and includes moment estimates for random Itô processes that are of independent interest. For deterministic coefficients, we provide unique strong solutions even if the drift fails to be of affine growth. The theory that we develop rests on Itô’s formula and leads to pth moment and pathwise exponential stability for \(p\ge 2\) with explicit Lyapunov exponents.

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.