A Lie Algebraic Approach to Numerical Integration of Stochastic Differential Equations

Authors:
Tetsuya Misawa
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
2001

Citing 0
Cited 4

Numerical integration of stochastic differential equations: weak second-order mid-point scheme for application in the composition PDF method

Journal of Computational Physics
A class of orthogonal integrators for stochastic differential equations

Journal of Computational and Applied Mathematics
A class of orthogonal integrators for stochastic differential equations

Journal of Computational and Applied Mathematics
Discrete Gradient Approach to Stochastic Differential Equations with a Conserved Quantity

SIAM Journal on Numerical Analysis

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Abstract

In this article, "composition methods (or operator splitting methods)" for autonomous stochastic differential equations (SDEs) are formulated to produce numerical approximation schemes for the equations. In the proposed methods, the exponential map, which is given by the solution of an SDE, is approximated by composition of the stochastic flows derived from simpler and exactly integrable vector field operators having stochastic coefficients. The local and global errors of the numerical schemes derived from the stochastic composition methods are investigated. The new schemes are advantageous to preserve the special character of SDEs numerically and are useful for approximations of the solutions to stochastic nonlinear equations. To examine their superiority, several numerical simulations on the basis of the proposed schemes are carried out for SDEs which arise in mathematical finance and stochastic Hamiltonian dynamical systems.