Exponential Ergodicity of Non-Lipschitz Multivalued Stochastic Differential Equations

TL;DR

This paper proves that solutions to certain complex stochastic differential equations with multivalued components converge exponentially fast to a steady state, ensuring long-term stability of the system.

Contribution

It establishes exponential ergodicity for elliptic multivalued stochastic differential equations, a novel result for this class of non-Lipschitz systems.

Findings

Transition probabilities converge exponentially fast.

Solutions exhibit long-term stability.

Provides theoretical foundation for multivalued SDEs.

Abstract

We prove the exponential ergodicity of the transition probabilities of solutions to elliptic multivalued stochastic differential equations.