Absolute Continuity of the Laws of Perturbed Diffusion Processes and Perturbed Reflected Diffusion Processes
Wen Yue, Tusheng Zhang
TL;DR
This paper proves that the probability laws of certain perturbed diffusion and reflected diffusion processes are absolutely continuous, using Malliavin calculus as the main analytical tool.
Contribution
It establishes absolute continuity of laws for perturbed diffusion processes and reflected diffusion processes, advancing the understanding of their probabilistic properties.
Findings
Laws are absolutely continuous w.r.t. Lebesgue measure
Malliavin calculus is effective for this analysis
Results apply to both diffusion and reflected diffusion processes
Abstract
In this paper, we prove that the laws of perturbed diffusion processes and perturbed reflected diffusion processes are absolutely continuous with respect to the Lebesgue measure. The main tool we use is the Malliavin calculus.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Stochastic processes and statistical mechanics