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.
- stochastic differential equations
- the Girsanov transformation
- nonlinear partial differential equation
- diffusion processes
Truman, A., Wang, F., Wu, J., & Yang, W. (2012). A link of stochastic differential equations to nonlinear parabolic equations. Science in China Series A: Mathematics, 55(10), 1971-1976. https://doi.org/10.1007/s11425-012-4463-2