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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Truman, A., Wang, F., Wu, J. et al. A link of stochastic differential equations to nonlinear parabolic equations. Sci. China Math. 55, 1971–1976 (2012). https://doi.org/10.1007/s11425-012-4463-2
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DOI: https://doi.org/10.1007/s11425-012-4463-2
Keywords
- stochastic differential equations
- the Girsanov transformation
- nonlinear partial differential equation
- diffusion processes