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

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...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 127; no. 2; pp. 359 - 384
Main Author Kusuoka, Seiichiro
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2017
Subjects
Density function
Gaussian two-sided bounds
Path-dependent
Stochastic differential equation
Path-dependent
60H10
Density function
Gaussian two-sided bounds
60J35
Stochastic differential equation
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2016.06.011