Continuous-time random walks for the numerical solution of stochastic differential equations / Nawaf Bou-Rabee, Eric Vanden-Eijnden.

Format:

Book

Author/Creator:

Bou-Rabee, Nawaf, author.

Vanden-Eijnden, Eric, author.

Series:

Memoirs of the American Mathematical Society ; Number 1228.

Memoirs of the American Mathematical Society ; Number 1228

Language:

English

Subjects (All):

Stochastic differential equations--Numerical solutions.

Stochastic differential equations.

Random walks (Mathematics).

Physical Description:

1 online resource (v,124 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, RI : American Mathematical Society, [2018]

Summary:

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be realized exactly using a Monte Carlo method. In this construction the jump size of the approximation can be bounded uniformly in space, which often guarantees that the schemes are numerically stable for both finite and long time simulation of SDEs.

Contents:

Introduction

Algorithms

Examples & applications

Analysis on gridded state spaces

Analysis on gridless state spaces

Tridiagonal case

Conclusion and outlook.

Notes:

Description based on print version record.

Includes bibliographical references.

ISBN:

1-4704-4919-6