International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2000 / Article

Open Access

Volume 13 |Article ID 609458 | https://doi.org/10.1155/S1048953300000216

Philippe Briand, René Carmona, "BSDEs with polynomial growth generators", International Journal of Stochastic Analysis, vol. 13, Article ID 609458, 32 pages, 2000. https://doi.org/10.1155/S1048953300000216

BSDEs with polynomial growth generators

Received01 Jul 1998
Revised01 Jul 1999

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.

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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