Smooth density for the Solution of Scalar SDEs with Locally Lipschitz Coefficients under Hörmander Condition

2013/09/03 by Tahmasebi, Mahdieh
#60H07 (Primary) 60H10 #62G07 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1309.0623

Abstract

In this paper the existence of a smooth density is proved for the solution of an SDE, with locally Lipschitz coefficients and semi-monotone drift, under Hörmander condition. We prove the nondegeneracy condition for the solution of the SDE, from it an integration by parts formula would result in the Wiener space. To this end we construct a sequence of SDEs with globally Lipschitz coefficients whose solutions converge to the original one and use some Lyapunov functions to show the uniformly boundedness of the p-moments of the solutions and their Malliavin derivatives.

Related

• Integration by Parts Formula and Smoothness of Densities of Solutions to SDEs with Locally Lipschitz Coefficients
• Exponential bounds for the density of the law of the solution of a SDE with locally Lipschitz coefficients
• Weak Differentiability of Solutions to SDEs With Semi-Monotone Drifts
• Smoothness of densities for path-dependent SDEs under Hörmander's condition
• Smoothing properties of McKean-Vlasov SDEs