Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion

Tom&#x000e1;s CARABALLO; Mamadou Abdoul DIOP

doi:10.1007/s11464-013-0300-3

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Front. Math. China ›› 2013, Vol. 8 ›› Issue (4) : 745-760. DOI: 10.1007/s11464-013-0300-3

RESEARCH ARTICLE

Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion

Tomás CARABALLO¹ ,
Mamadou Abdoul DIOP²

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Abstract

This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion B^H, with Hurst parameter H∈ (1/2, 1). We use the theory of resolvent operators developed by R. Grimmer to show the existence of mild solutions. An example is provided to illustrate the results of this work.

Keywords

Resolvent operator / C₀-semigroup / Wiener process / mild solution / fractional Brownian motion

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Tomás CARABALLO, Mamadou Abdoul DIOP. Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion. Front Math Chin, 2013, 8(4): 745‒760 https://doi.org/10.1007/s11464-013-0300-3

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