Gaussian estimates for the solutions of some one-dimensional stochastic equations
Nguyen, Tien Dung
Torrisi, Giovanni Luca
Date of Issue2015
School of Physical and Mathematical Sciences
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.
© 2015 Springer Science+Business Media Dordrecht. This is the author created version of a work that has been peer reviewed and accepted for publication by Potential Analysis, Springer Science+Business Media Dordrecht. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [Article DOI: http://dx.doi.org/10.1007/s11118-015-9472-7].