Gaussian Estimates for the Solutions of Some One-dimensional Stochastic Equations
Using covariance identities based on the Clark-Ocone representation formula we derive Gaussian density bounds and tail estimates for the probability law of the solutions of several types of stochastic differential equations, including Stratonovich equations with boundary condition and irregular drifts, and equations driven by fractional Brownian motion. Our arguments are generally simpler than the existing ones in the literature as our approach avoids the use of the inverse of the Ornstein-Uhlenbeck operator.
KeywordsMalliavin calculus Clark-Ocone formula Probability bounds Fractional Brownian motion
Mathematical Subject Classification (2010)60F05 60G57 60H07
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