In this paper we explain the notion of stochastic backward differential equations and its relationship with classical (backward) parabolic differential equations of second order. The paper contains a mixture of stochastic processes like Markov processes and martingale theory and semi-linear partial differential equations of parabolic type. Some emphasis is put on the fact that the whole theory generalizes Feynman-Kac formulas. A new method of proof of the existence of solutions is given. All the existence arguments are based on rather precise quantitative estimates.
CITATION STYLE
Van Casteren, J. A. (2007). Feynman-Kac Formulas, Backward Stochastic Differential Equations and Markov Processes. In Functional Analysis and Evolution Equations (pp. 83–111). Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7794-6_6
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