Exponential bounds for the density of the law of the solution of a SDE with locally Lipschitz coefficients

Abstract

Under the uniform Hörmander’s hypothesis we study smoothness and exponential bounds of the density of the law of the solution of a stochastic differential equation (SDE) with locally Lipschitz drift that satisfy a monotonicity condition. To obtain estimates for the Malliavin covariance matrix and its inverse, we extend the approach in to SDEs with non-globally Lipschitz coefficients. As in, to avoid non-integrability problems we use results about Malliavin differentiability based on the concepts of Ray Absolute Continuity and Stochastic Gateâux differentiability.