A class of second-order McKean–Vlasov stochastic evolution equations driven by fractional Brownian motion and Poisson jumps. (15th January 2020) - McKibben, Mark A.; Webster, Micah
Abstract: This paper focuses on a class of second-order McKean–Vlasov stochastic evolution equations driven by a fractional Brownian motion and Poisson jumps. Specifically, we allow nonlinearities and the jump term to depend not only of the state of the solution, but also on the corresponding probability law of the state. The global existence and uniqueness of mild solutions is established under various growth conditions, and a related stability result is discussed. An example is presented to illustrate the applicability of the theory.