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

Dai Taguchi and Akihiro Tanaka

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5243-5289

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.

Keywords: Probability density function; Maruyama–Girsanov theorem; Gaussian two-sided bound; Parametrix method; Euler–Maruyama scheme; Unbiased simulation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2020.03.006

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