On the generalized McKean–Vlasov stochastic differential equations driven by time-changed Brownian motion

Abstract

In this paper, we investigate a class of generalized time-changed McKean–Vlasov stochastic differential equations with two drift terms, one driven by the random change Et and the other driven by nonrandom time t. Firstly, we consider the existence and uniqueness of the solution to the considered equations under some appropriate conditions. Meanwhile, by developing some generalized Itô’s formulas, some sufficient conditions are provided to guarantee the solutions to be stable in several different senses in terms of Lyapunov functions. Subsequently, we explore the non-confluence property of the solution to the considered equations by establishing some so-called time-changed Gronwall-like inequalities. Finally, some numerical examples are provided to demonstrate the effectiveness and applicability of the proposed theoretical results.