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Theses

Discretizations associated to a process in a domain and probabilistic numerical schemes for quasilinear parabolic PDEs

Abstract : The work in this thesis concerns the discretization of a process in a domain and probabilistic numerical approximations of quasilinear parabolic PDEs. Regarding the first topic, we first obtained a lower and upper bound for the error associated to a killed hypoelliptic diffusion process approximated by its discretely killed Euler scheme, cf. Chapter 1. Then, in the non Markovian framework of Ito processes, we obtained a bound for the error associated to the discretization of the exit time using original martingale techniques, cf. Chapter 2. Eventually, in the particular case of Brownian motion in an orthant, we obtained an error expansion and an acceleration of convergence method based on a suitable correction of the domain, cf. Chapter 3. Concerning the second topic, we proposed an algorithm easy to implement to approximate the solution of quasilinear parabolic PDEs. We also established a speed of convergence. This method consists in discretizing the Forward Backward Stochastic Differential Equation (FBSDE) that allows to give a probabilistic interpretation of the PDE, cf. Chapter 4.
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https://tel.archives-ouvertes.fr/tel-00008769
Contributor : Stephane Menozzi <>
Submitted on : Monday, March 14, 2005 - 1:27:05 PM
Last modification on : Wednesday, December 9, 2020 - 3:06:01 PM
Long-term archiving on: : Friday, September 14, 2012 - 12:00:46 PM

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  • HAL Id : tel-00008769, version 1

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Stephane Menozzi. Discretizations associated to a process in a domain and probabilistic numerical schemes for quasilinear parabolic PDEs. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2004. English. ⟨tel-00008769⟩

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