The Annals of Applied Probability

Simulation of diffusions by means of importance sampling paradigm

Madalina Deaconu and Antoine Lejay

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Abstract

The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with importance sampling techniques.

The first interest of this approach is that the weights can be easily computed from the density of the one-dimensional Brownian motion. Compared to the Euler scheme this method allows one to obtain a more accurate approximation of diffusions when one has to consider complex boundary conditions. The method provides also an interesting alternative to performing variance reduction techniques and simulating rare events.

Article information

Source
Ann. Appl. Probab., Volume 20, Number 4 (2010), 1389-1424.

Dates
First available in Project Euclid: 20 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1279638790

Digital Object Identifier
doi:10.1214/09-AAP659

Mathematical Reviews number (MathSciNet)
MR2676943

Zentralblatt MATH identifier
1204.60075

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 65C 65M 68U20: Simulation [See also 65Cxx]

Keywords
Stochastic differential equations Monte Carlo methods random walk on squares random walk on rectangles variance reduction simulation of rare events Dirichlet/Neumann problems

Citation

Deaconu, Madalina; Lejay, Antoine. Simulation of diffusions by means of importance sampling paradigm. Ann. Appl. Probab. 20 (2010), no. 4, 1389--1424. doi:10.1214/09-AAP659. https://projecteuclid.org/euclid.aoap/1279638790


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