A class of second-order McKean–Vlasov stochastic evolution equations driven by fractional Brownian motion and Poisson jumps. (15th January 2020)

• Record Type: Journal Article
• Authors: McKibben, Mark A.; Webster, Micah
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 2(2020)
• Page Start: 391
• Page End: 406
• Publication Date: 2020-01-15
• Subjects: Stochastic evolution equation -- McKean–Vlasov -- Fractional Brownian motion -- Second-order equation -- Poisson jumps -- Cosine family; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.07.013
• Languages: English
• ISSNs: 0898-1221

Abstract

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.