Smooth densities of the laws of perturbed diffusion processes

Lihu Xu; Wen Yue; Tusheng Zhang

doi:10.1016/j.spl.2016.07.016

Smooth densities of the laws of perturbed diffusion processes

Lihu Xu, Wen Yue^*, Tusheng Zhang

^*Corresponding author for this work

The University of Manchester

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Abstract

Under some regularity conditions on b, σ and α, we prove that the solution of the following perturbed stochastic differential equation X_t=x+∫₀ ^tb(X_s)ds+∫₀ ^tσ(X_s)dB_s+αsup0≤s≤tX_s,α0, where t₀>0 is some finite number.

Original language	English
Pages (from-to)	55-62
Number of pages	8
Journal	Statistics and Probability Letters
Volume	119
Early online date	25 Jul 2016
DOIs	https://doi.org/10.1016/j.spl.2016.07.016
Publication status	Published - 1 Dec 2016

Keywords

Malliavin differentiability
Perturbed diffusion processes
Smooth density

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10.1016/j.spl.2016.07.016

XuYueZhang151105Accepted author manuscript, 103 KB

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title = "Smooth densities of the laws of perturbed diffusion processes",

abstract = "Under some regularity conditions on b, σ and α, we prove that the solution of the following perturbed stochastic differential equation Xt=x+∫0 tb(Xs)ds+∫0 tσ(Xs)dBs+αsup0≤s≤tXs,α0, where t0>0 is some finite number.",

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AU - Xu, Lihu

AU - Yue, Wen

AU - Zhang, Tusheng

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N2 - Under some regularity conditions on b, σ and α, we prove that the solution of the following perturbed stochastic differential equation Xt=x+∫0 tb(Xs)ds+∫0 tσ(Xs)dBs+αsup0≤s≤tXs,α0, where t0>0 is some finite number.

AB - Under some regularity conditions on b, σ and α, we prove that the solution of the following perturbed stochastic differential equation Xt=x+∫0 tb(Xs)ds+∫0 tσ(Xs)dBs+αsup0≤s≤tXs,α0, where t0>0 is some finite number.

KW - Malliavin differentiability

KW - Perturbed diffusion processes

KW - Smooth density

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DO - 10.1016/j.spl.2016.07.016

M3 - Article

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VL - 119

SP - 55

EP - 62

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Smooth densities of the laws of perturbed diffusion processes

Abstract

Keywords

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