Smooth densities of the laws of perturbed diffusion processes
Probability
2016-01-26 v1
Abstract
Under some regularity conditions on , and , we prove that the following perturbed stochastic differential equation \begin{equation} X_t=x+\int_0^t b(X_s)ds+\int_0^t \sigma(X_s) dB_s+\alpha \sup_{0 \le s \le t} X_s, \ \ \ \alpha<1 \end{equation} admits smooth densities for all , where is some finite number.
Keywords
Cite
@article{arxiv.1601.06275,
title = {Smooth densities of the laws of perturbed diffusion processes},
author = {Lihu Xu and Wen Yue and Tusheng Zhang},
journal= {arXiv preprint arXiv:1601.06275},
year = {2016}
}