Transportation inequalities for stochastic delay evolution equations driven by fractional Brownian motion

Abstract

We discuss stochastic functional partial differential equations and neutral partial differential equations of retarded type driven by fractional Brownian motion with Hurst parameter H>1/2. Using the Girsanov transformation argument, we establish the quadratic transportation inequalities for the law of the mild solution of those equations driven by fractional Brownian motion under the L² metric and the uniform metric.

Keywords

Transportation inequality / Girsanov transformation / delay stochastic partial differential equation (SPDE) / fractional Brownian motion (fBm)

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Higher Education Press and Springer-Verlag Berlin Heidelberg