The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion

作者：Caraballo T^*; Garrido Atienza M J; Taniguchi T

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(11): 3671-3684.

DOI：10.1016/j.na.2011.02.047

• Delay stochastic PDEs
• Fractional Brownian motion
• Exponential decay in mean square

In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion B(Q)(H)(t):
dX(t) = (AX(t) + f (t, X(t)))dt + g(t)dB(Q)(H)(t),
with Hurst parameter H is an element of (1/2, 1). We also consider the existence of weak solutions.

• 出版日期2011-7