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 in R. Grimmer [5] to show the existence of mild solutions. An example is provided to illustrate the results of this work.2010 MSC: 60H15; 35R60.
We study the homogenization problem for a random parabolic operator with coefficients rapidly oscillating in both the space and time variables and with a large highly oscillating nonlinear potential, in a general stationary and mixing random media, which is periodic in space. It is shown that a solution of the corresponding Cauchy problem converges in law to a solution of a limit stochastic PDE.
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