4 papers
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…
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…
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.…
Small perturbations may change the sign of Lyapunov exponents for linear SDEs
Xianjin Cheng, Zhenxin Liu, Lixin Zhang
In this paper, we study the existence of -dimensional linear stochastic differential equations (SDEs) such that the sign of Lyapunov exponents is changed under an exponentially…