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Journal articles

BSDEs with polynomial growth generators

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.
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https://hal.archives-ouvertes.fr/hal-01547366
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Submitted on : Monday, June 26, 2017 - 3:58:27 PM
Last modification on : Wednesday, April 6, 2022 - 3:48:04 PM

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Philippe Briand, René Carmona. BSDEs with polynomial growth generators. Journal of Applied Mathematics and Stochastic Analysis, North Atlantic Science Publishing Company, 2000, 13 (3), pp.207 - 238. ⟨10.1155/S1048953300000216⟩. ⟨hal-01547366⟩

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