Fractional Measure-dependent Nonlinear Second-order Stochastic Evolution Equations with Poisson Jumps

Abstract

This paper focuses on a nonlinear second-order stochastic evolution equations driven by a fractional Brownian motion (fBm) with Poisson jumps and which is dependent upon a family of probability measures. The global existence 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.

Keywords

• stochastic evolution equation
• fractional brownian motion
• second-order equation
• poisson jumps
• cosine family
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