Abstract
In this article, we study the existence and uniqueness of square-mean piecewise almost periodic solutions to a class of impulsive stochastic functional differential equations driven by fractional Brownian motion. Moreover, the stability of the mild solution is obtained. To illustrate the results obtained in the paper, an impulsive stochastic functional differential equation driven by fractional Brownian motion is considered.
Highlights
Impulsive systems arise naturally in a wide variety of evolutionary processes in which states are changed abruptly at certain moments of time
We study the existence and uniqueness of square-mean piecewise almost periodic solutions to a class of impulsive stochastic functional differential equations driven by fractional Brownian motion
Arthi et al [2] considered the existence and exponential stability for neutral stochastic integrodifferential equations with impulses driven by fractional Brownian motion, and Caraballo [3] studied the existence of mild solutions to stochastic delay evolution equations with fractional Brownian motions (fBms) and impulses
Summary
Impulsive systems arise naturally in a wide variety of evolutionary processes in which states are changed abruptly at certain moments of time. Arthi et al [2] considered the existence and exponential stability for neutral stochastic integrodifferential equations with impulses driven by fractional Brownian motion (fBm), and Caraballo [3] studied the existence of mild solutions to stochastic delay evolution equations with fBm and impulses. We are concerned with the existence and stability of almost periodic mild solutions to the following impulsive stochastic functional differential system driven by fBm with Hurst index H ∈(1/2, 1):. There is no strong solution for stochastic partial delay differential equations driven by fractional Brownian motion. An example is provided to illustrate the effectiveness of the results
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