Feynman-Kac Formulas, Backward Stochastic Differential Equations and Markov Processes

Jan A. Van Casteren ()
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Jan A. Van Casteren: University of Antwerp, Department of Mathematics and Computer Science

A chapter in Functional Analysis and Evolution Equations, 2007, pp 83-111 from Springer

Abstract: Abstract 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.

Keywords: Brownian Motion; Markov Process; Monotonicity Condition; Unique Pair; Malliavin Calculus (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_6

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DOI: 10.1007/978-3-7643-7794-6_6

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