Abstract

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g. the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

Original languageEnglish (US)
Pages (from-to)207-238
Number of pages32
JournalJournal of Applied Mathematics and Stochastic Analysis
Volume13
Issue number3
DOIs
StatePublished - Jan 1 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Backward Stochastic Differential Equation
  • Monotonicity
  • Polynomial Generator

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