The walk on moving spheres: A new tool for simulating Brownian motion’s exit time from a domain

Autor: Sylvain Maire, Samuel Herrmann, Madalina Deaconu
Přispěvatelé: TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Laboratoire Modélisation et Signal (LMS), Université de Toulon (UTLN)-ISITV, Probabilités et statistiques, Institut Élie Cartan de Lorraine ( IECL ), Université de Lorraine ( UL ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Lorraine ( UL ) -Centre National de la Recherche Scientifique ( CNRS ), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique ( Inria ), Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire des Sciences de l'Information et des Systèmes ( LSIS ), Aix Marseille Université ( AMU ) -Université de Toulon ( UTLN ) -Arts et Métiers Paristech ENSAM Aix-en-Provence-Centre National de la Recherche Scientifique ( CNRS ), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS), TO Simulate and CAlibrate stochastic models ( TOSCA ), Inria Sophia Antipolis - Méditerranée ( CRISAM ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut Élie Cartan de Lorraine ( IECL ), Laboratoire Modélisation et Signal ( LMS ), Université de Toulon ( UTLN ) -ISITV, TOSCA
Rok vydání: 2017
Předmět:
[ MATH ] Mathematics [math]
[ INFO ] Computer Science [cs]
Brownian hitting time
General Computer Science
Bessel process
Boundary (topology)
hitting time
01 natural sciences
Bessel processes
Theoretical Computer Science
010104 statistics & probability
symbols.namesake
Position (vector)
FOS: Mathematics
0101 mathematics
Brownian motion
Mathematics
Numerical Analysis
Series (mathematics)
Boundary
Applied Mathematics
Probability (math.PR)
Mathematical analysis
Hitting time
65C20
65C05
Algorithm
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
010101 applied mathematics
Distribution (mathematics)
Walk on moving spheres method
Modeling and Simulation
1st-Passage Density
symbols
numerical algorithm
[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Mathematics - Probability
Bessel function
Zdroj: Mathematics and Computers in Simulation
9th IMACS Seminar on Monte Carlo Methods (MCM)
9th IMACS Seminar on Monte Carlo Methods (MCM), Jul 2013, Annecy le Vieux, France. pp.28-38, ⟨10.1016/j.matcom.2015.07.004⟩
9th IMACS Seminar on Monte Carlo Methods (MCM), Jul 2013, Annecy le Vieux, France. ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS, 135, pp.28-38, 2017, 〈http://www.sciencedirect.com/science/article/pii/S0378475415001366〉. 〈10.1016/j.matcom.2015.07.004〉
Mathematics and Computers in Simulation, Elsevier, 2017, 135, pp.28--38. 〈https://doi.org/10.1016/j.matcom.2015.07.004〉
ISSN: 0378-4754
DOI: 10.1016/j.matcom.2015.07.004
Popis: International audience; In this paper we introduce a new method for the simulation of the exit time and exit position of a (delta-dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time schemes as well as inversion of complicated series. The method, called walk on moving spheres algorithm, was first introduced for hitting times of Bessel processes. In this study this method is adapted and developed for the first time for the Brownian motion hitting times. The idea is to use the connexion between the (delta-dimensional Bessel process and the (delta-dimensional Brownian motion thanks to an explicit Bessel hitting time distribution associated with a particular curved boundary. This allows to build a fast and accurate numerical scheme for approximating the hitting time. We introduce also an overview of existing methods for the simulation of the Brownian hitting time and perform numerical comparisons with existing methods. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Databáze: OpenAIRE
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