Displaying similar documents to “Euler schemes and half-space approximation for the simulation of diffusion in a domain”

Probabilistic methods for semilinear partial differential equations. Applications to finance

Dan Crisan, Konstantinos Manolarakis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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With the pioneering work of [Pardoux and Peng, (1990) 55–61; Pardoux and Peng, (1992) 200–217]. We have at our disposal stochastic processes which solve the so-called . These processes provide us with a Feynman-Kac representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear in many applications in the field of Mathematical Finance. Therefore there is a great interest among both practitioners and theoreticians...

Approximation of the Snell envelope and american options prices in dimension one

Vlad Bally, Bruno Saussereau (2002)

ESAIM: Probability and Statistics

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We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.

Diffusion Monte Carlo method: Numerical Analysis in a Simple Case

Mohamed El Makrini, Benjamin Jourdain, Tony Lelièvre (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example,...

Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence

Abdel Berkaoui, Mireille Bossy, Awa Diop (2008)

ESAIM: Probability and Statistics

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We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form | x | α , α ∈ [ 1 / 2 , 1 ) . In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.

Numerical schemes for multivalued backward stochastic differential systems

Lucian Maticiuc, Eduard Rotenstein (2012)

Open Mathematics

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We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: d Y t + F ( t , X t , Y t , Z t ) d t ∈ ∂ φ ( Y t ) d t + Z t d W t , where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward...