A link of stochastic differential equations to nonlinear parabolic equations

Aubrey Truman; FengYu Wang; JiangLun Wu; Wei Yang

doi:10.1007/s11425-012-4463-2

A link of stochastic differential equations to nonlinear parabolic equations

Aubrey Truman, FengYu Wang, JiangLun Wu, Wei Yang

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Using Girsanov transformation, we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type, in such a manner that the obtained Burgers-KPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation. Our assertion also holds for SDEs on a connected differential manifold.

Original language	English
Pages (from-to)	1971-1976
Number of pages	6
Journal	Science in China Series A: Mathematics
Volume	55
Issue number	10
DOIs	https://doi.org/10.1007/s11425-012-4463-2
Publication status	Published - 1 Oct 2012

Keywords

stochastic differential equations
the Girsanov transformation
nonlinear partial differential equation
diffusion processes

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10.1007/s11425-012-4463-2

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title = "A link of stochastic differential equations to nonlinear parabolic equations",

abstract = "Using Girsanov transformation, we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type, in such a manner that the obtained Burgers-KPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation. Our assertion also holds for SDEs on a connected differential manifold.",

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AU - Truman, Aubrey

AU - Wang, FengYu

AU - Wu, JiangLun

AU - Yang, Wei

N1 - I have updated this entry

PY - 2012/10/1

Y1 - 2012/10/1

N2 - Using Girsanov transformation, we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type, in such a manner that the obtained Burgers-KPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation. Our assertion also holds for SDEs on a connected differential manifold.

AB - Using Girsanov transformation, we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type, in such a manner that the obtained Burgers-KPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation. Our assertion also holds for SDEs on a connected differential manifold.

KW - stochastic differential equations

KW - the Girsanov transformation

KW - nonlinear partial differential equation

KW - diffusion processes

U2 - 10.1007/s11425-012-4463-2

DO - 10.1007/s11425-012-4463-2

M3 - Article

SN - 1006-9283

VL - 55

SP - 1971

EP - 1976

JO - Science in China Series A: Mathematics

JF - Science in China Series A: Mathematics

IS - 10

ER -

A link of stochastic differential equations to nonlinear parabolic equations

Abstract

Keywords

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