Equations différentielles stochastiques progressives rétrogrades couplées : équations aux dérivées partielles et discrétisation

Abstract : This thesis deals with the forward backward stochastic differential equations, in particular those with a coefficient of progressive diffusion which depends on all unknowns of the problem. We propose an original way to get onto this subject, letting us to reobtain some classical results of existence and uniqueness in the spirit of Pardoux-Tang and Yong's results, and to find a probabilistic representation of a new class of parabolic PDE, in which derivation coefficient of order 2 depends on the gradient of the solution. We also propose an iterative discretization scheme. We prove its convergence and give an evaluation of the error on a particular example.
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Submitted on : Saturday, December 17, 2005 - 7:38:23 PM
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Olivier Riviere. Equations différentielles stochastiques progressives rétrogrades couplées : équations aux dérivées partielles et discrétisation. Mathématiques [math]. Université René Descartes - Paris V, 2005. Français. ⟨tel-00011231⟩

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