Gauss-quadrature method for one-dimensional mean-field SDEs

Peter Kloeden, Tony Shardlow

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Mean-field SDEs, also known as McKean--Vlasov equations, are stochastic differential equations where the drift and diffusion depend on the current distribution in addition to the current position. We describe an efficient numerical method for approximating the distribution at time $t$ of the solution to the initial-value problem for one-dimensional mean-field SDEs. The idea is to time march (e.g., using the Euler--Maruyama time-stepping method) an $m$-point Gauss-quadrature rule. With suitable regularity conditions, convergence with first order is proved for Euler--Maruyama time stepping. We also estimate the work needed to achieve a given accuracy in terms of the smoothness of the underlying problem. Numerical experiments are given, which show the effectiveness of this method as well as two second-order time-stepping methods. The methods are also effective for ordinary SDEs in one dimension, as we demonstrate by comparison with the multilevel Monte Carlo method.


Read More: http://epubs.siam.org/doi/10.1137/16M1095688
Original languageEnglish
Pages (from-to) A2784–A2807
Number of pages23
JournalSIAM Journal on Scientific Computing
Volume39
Issue number6
Early online date30 Nov 2017
DOIs
Publication statusPublished - 6 Dec 2017

Fingerprint Dive into the research topics of 'Gauss-quadrature method for one-dimensional mean-field SDEs'. Together they form a unique fingerprint.

Cite this