TY - JOUR

T1 - Probability density function of SDEs with unbounded and path-dependent drift coefficient

AU - Taguchi, Dai

AU - Tanaka, Akihiro

N1 - Publisher Copyright:
Copyright © 2018, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2018/11/17

Y1 - 2018/11/17

N2 - 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

AB - 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

KW - Euler-maruyama scheme

KW - Gaussian two-sided bound

KW - Hölder continuity

KW - Maruyama-girsanov theorem

KW - Parametrix method

KW - Probability density function

KW - Unbiased simulation

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M3 - Article

AN - SCOPUS:85093732405

JO - [No source information available]

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SN - 0402-1215

ER -