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On time‐dependent stochastic evolution equations driven by fractional Brownian motion in a Hilbert space with finite delay
Author(s) -
Ren Yong,
Cheng Xing,
Sakthivel Rathinasamy
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2967
Subject(s) - fractional brownian motion , mathematics , uniqueness , hurst exponent , wiener process , brownian motion , hilbert space , mathematical analysis , class (philosophy) , stochastic process , statistics , computer science , artificial intelligence
In this paper, we show the existence and uniqueness of the mild solution for a class of time‐dependent stochastic evolution equations with finite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion with Hurst parameter H ∈ (1 / 2,1). An example is provided to illustrate the theory. Copyright © 2013 John Wiley & Sons, Ltd.