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

  • Jan A. Van Casteren


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.


Brownian Motion Markov Process Monotonicity Condition Unique Pair Malliavin Calculus 
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© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Jan A. Van Casteren
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of AntwerpAntwerpBelgium

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