A link of stochastic differential equations to nonlinear parabolic equations

作者：Truman, Aubrey; Wang FengYu^*; Wu JiangLun; Yang Wei

来源：Science China Mathematics, 2012, 55(10): 1971-1976.

DOI：10.1007/s11425-012-4463-2

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

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.

• 出版日期2012-10
• 单位北京师范大学