Probability density function of SDEs with unbounded and path-dependent drift coefficient

Dai Taguchi, Akihiro Tanaka

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we first prove that the existence of a solution of SDEs under the assumptions that the drift coefficient is of linear growth and path-dependent, and diffusion coefficient is bounded, uniformly elliptic and Hölder continuous. We apply Gaussian upper bound for a probability density function of a solution of SDE without drift coefficient and local Novikov condition, in order to use Maruyama-Girsanov transformation. The aim of this paper is to prove the existence with explicit representations (under linear/super-linear growth condition), Gaussian two-sided bound and Hölder continuity (under sub-linear growth condition) of a probability density function of a solution of SDEs with path-dependent drift coefficient. As an application of explicit representation, we provide the rate of convergence for an Euler-Maruyama (type) approximation, and an unbiased simulation scheme.

MSC Codes 65C30, 62G07, 35K08, 60H35

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - Nov 17 2018

Keywords

  • Euler-maruyama scheme
  • Gaussian two-sided bound
  • Hölder continuity
  • Maruyama-girsanov theorem
  • Parametrix method
  • Probability density function
  • Unbiased simulation

ASJC Scopus subject areas

  • General

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