Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske
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引用次数: 0
Abstract
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.
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.
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