TY - JOUR

T1 - Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation

AU - Kusuoka, Seiichiro

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant number 25800054 .
Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - Density function

KW - Gaussian two-sided bounds

KW - Path-dependent

KW - Stochastic differential equation

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U2 - 10.1016/j.spa.2016.06.011

DO - 10.1016/j.spa.2016.06.011

M3 - Article

AN - SCOPUS:84996868109

SN - 0304-4149

VL - 127

SP - 359

EP - 384

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -