3 papers
math.DS2026
Continuity of measure-theoretic entropy for stochastic differential equations
Zhenxin Liu, Lixin Zhang
For stochastic differential equations, we establish a relationship between the measure-theoretic entropy of the stochastic flow and the rate of volume growth of stable submanifolds…
math.DS2024
Continuity of Lyapunov exponents for stochastic differential equations
Zhenxin Liu, Lixin Zhang
For non-autonomous linear stochastic differential equations (SDEs), we establish that the top Lyapunov exponent is continuous if the coefficients "almost" uniformly converge. For a…
math.DS2024
The multiplicative ergodic theorem for McKean-Vlasov SDEs
Xianjin Cheng, Zhenxin Liu, Lixin Zhang
In this paper, we establish the multiplicative ergodic theorem for McKean-Vlasov stochastic differential equations, in which the Lyapunov exponent is defined using the upper limit.…