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

Cristina Anton

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arXiv · 2407.14756

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

Cristina Anton

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Abstract

Under the uniform H\"{o}rmander'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 avoid non-integrability problems we use results about Malliavin differentiability based on the concepts of Ray Absolute Continuity and Stochastic Gate\^aux differentiability.

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Cristina Anton. 2024-07-20. Exponential bounds for the density of the law of the solution of a SDE with locally Lipschitz coefficients. https://arxiv.org/abs/2407.14756

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