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. In this paper, we consider the stochastic analysis for fractional Brownian bridge measures. We first give an integration by parts formula for such measures by Bismut’s method and a pull back formula. Using this integration by parts formula, we then obtain a generalized Clark-Ocone martingale representation theorem for fractional Brownian bridge measures. Consequently, a Logarithmic-Sobolev inequality is derived by the martingale representation theorem for such measures.

On Martingale Representation and Logarithmic-Sobolev Inequality for Fractional Brownian Bridge Measures