Result: Weak approximation of killed diffusion using Euler schemes
Title:
Weak approximation of killed diffusion using Euler schemes
Authors:
Source:
Stochastic processes and their applications. 87(2):167-197
Publisher Information:
Amsterdam: Elsevier Science, 2000.
Publication Year:
2000
Physical Description:
print, 26 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Analyse stochastique, Stochastic analysis, Approximation, Aproximación, Calcul Malliavin, Malliavin calculus, Cálculo Malliavin, Ellipticité, Ellipticity, Elipticidad, Estimation erreur, Error estimation, Estimación error, Modèle n dimensions, Multidimensional model, Modelo n dimensiones, Mouvement brownien, Brownian motion, Movimiento browniano, Méthode Monte Carlo, Monte Carlo method, Método Monte Carlo, Processus diffusion, Diffusion process, Proceso difusión, Projection orthogonale, Orthogonal projection, Proyección ortogonal, Schéma Euler, Euler scheme, Esquema Euler, Taux convergence, Convergence rate, Relación convergencia, Temps local, Local time, Tiempo local, Développement erreur, Error expansion, Formule Itô, Itô formula, Formule Tanaka, Tanaka formula
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Laboratoire de Probabilités et Modèles Aléatoires. Case 7012, Université Paris VII. 2, place Jussieu, 75251 Paris, France
ISSN:
0304-4149
Rights:
Copyright 2000 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.1357022
Database:
PASCAL Archive
Further Information
We study the weak approximation of a multidimensional diffusion (Xt)0≤t≤T killed as it leaves an open set D, when the diffusion is approximated by its continuous Euler scheme (Xt)0≤t≤T or by its discrete one (Xt1)0≤i≤N, with discretization step T/N. If we set τ:=inf{t > 0: Xt ¬∈ D} and τc:=inf{t > 0: Xt ¬∈ D}, we prove that the discretization error Ex[1T<τc f(XT)]-Ex[1T<τ f(XT)] can be expanded to the first order in N- provided support or regularity conditions on f. For the discrete scheme, if we set τd:=inf{ti > 0: Xti ¬∈ D}, the error Ex[1T<τd f(XT)]-Ex[1T<τ f(XT)] is of order N-1 under analogous assumptions on f. This rate of convergence is actually exact and intrinsic to the problem of discrete killing time.