A link of stochastic differential equations to nonlinear parabolic equations

Truman, Aubrey and Wang, FengYu and Wu, JiangLun and Yang, Wei (2012) A link of stochastic differential equations to nonlinear parabolic equations. Science in China Series A: Mathematics, 55 (10). pp. 1971-1976. ISSN 1006-9283

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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.