Martingale Representation and Logarithmic-Sobolev Inequality for Fractional Ornstein-Uhlenbeck Measure

Abstract

In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such measure, we establish a martingale representation theorem and consequently obtain the Logarithmic-Sobolev inequality. To this end, we also present the integration by parts formula for such measure, which is obtained via its pull back formula and the Bismut method.