Accurate stationary densities with partitioned numerical methods for stochastic differential equations

Burrage, Kevin and Lythe, Grant (2009) Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Siam Journal on Numerical Analysis, 47 3: 1601-1618.


Author Burrage, Kevin
Lythe, Grant
Title Accurate stationary densities with partitioned numerical methods for stochastic differential equations
Journal name Siam Journal on Numerical Analysis   Check publisher's open access policy
ISSN 0036-1429
1095-7170
Publication date 2009-04
Year available 2009
Sub-type Article (original research)
DOI 10.1137/060677148
Volume 47
Issue 3
Start page 1601
End page 1618
Total pages 18
Editor Thomas A Manteuffel
Place of publication Philadelphia, Pa., USA
Publisher SIAM Publications
Collection year 2010
Language eng
Subject 0103 Numerical and Computational Mathematics
C1
010103 Category Theory, K Theory, Homological Algebra
970101 Expanding Knowledge in the Mathematical Sciences
Abstract We devise explicit partitioned numerical methods for second–order-in-time scalar stochastic differential equations, using one Gaussian random variable per timestep. The construction proceeds by analysis of the stationary density in the case of constant-coefficient linear equations, imposing exact stationary statistics in the position variable and absence of correlation between position and velocity; the remaining error is in the velocity variable. A new two-stage “reverse leapfrog” method has good properties in the position variable and is symplectic in the limit of zero damping. Explicit new “Runge–Kutta leapfrog” methods are constructed, sharing the property that $q_{n+1}=q_n+\frac{1}{2}(p_n+p_{n+1})\Delta t$, whose mean-square velocity order increases with the number of stages. ©2009 Society for Industrial and Applied Mathematics
Keyword damped harmonic oscillators with noise
stationary distribution
stochastic Runge-Kutta methods
leapfrog methods
Q-Index Code C1
Q-Index Status Confirmed Code

 
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Created: Fri, 04 Sep 2009, 10:26:58 EST