Exponential bounds for the density of the law of the solution of an SDE with locally Lipschitz coefficients
Author
Faculty Advisor
Date
2025
Keywords
Malliavin covariance matrix, Hörmander’s condition, exponential bounds for density, monotone growth, stochastic differential equation
Abstract (summary)
Under the uniform Hörmander hypothesis, we study the smoothness and exponential bounds of the density of the law of the solution of a stochastic differential equation (SDE) with locally Lipschitz drift that satisfies a monotonicity condition. We extend the approach used for SDEs with globally Lipschitz coefficients and obtain estimates for the Malliavin covariance matrix and its inverse. Based on these estimates and using the Malliavin differentiability of any order of the solution of the SDE, we prove exponential bounds of the solution’s density law. These results can be used to study the convergence of implicit numerical schemes for SDEs.
Publication Information
Anton, C. (2025). Exponential Bounds for the Density of the Law of the Solution of an SDE with Locally Lipschitz Coefficients. Mathematics, 13(5), 798. https://doi.org/10.3390/math13050798
Notes
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Article
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Rights
Attribution (CC BY)
