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

Seiichiro Kusuoka

Research output: Contribution to journalArticle

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)359-384
Number of pages26
JournalStochastic Processes and their Applications
Issue number2
Publication statusPublished - Feb 1 2017



  • Density function
  • Gaussian two-sided bounds
  • Path-dependent
  • Stochastic differential equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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