Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation

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• 作者：Seiichiro Kusuoka ^{kusuoka@okayama-u.ac.jp}
• 关键词：60H10 ; 60J35
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：127
• 期：2
• 页码：359-384
• 全文大小：346 K
• 卷排序：127

文摘

We consider Markovian stochastic differential equations with low regular coefficients and their perturbations by adding a measurable bounded path-dependent drift term. When we assume the diffusion coefficient matrix is uniformly positive definite, then the solution to the perturbed equation is given by the Girsanov transformation of the original equation. By using the expression we obtain the Gaussian two-sided bounds and the continuity of the density function of the solution to the perturbed equation. We remark that the perturbation in the present paper is a stochastic analogue to the perturbation in the operator analysis.