### A Milstein Scheme for SPDEs

Jentzen A, Röckner M (2015)
Foundations of Computational Mathematics 15(2): 313-362.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Einrichtung
Abstract / Bemerkung
This article studies an infinite-dimensional analog of Milstein's scheme for finite-dimensional stochastic ordinary differential equations (SODEs). The Milstein scheme is known to be impressively efficient for SODEs which fulfill a certain commutativity type condition. This article introduces the infinite-dimensional analog of this commutativity type condition and observes that a certain class of semilinear stochastic partial differential equation (SPDEs) with multiplicative trace class noise naturally fulfills the resulting infinite-dimensional commutativity condition. In particular, a suitable infinite-dimensional analog of Milstein's algorithm can be simulated efficiently for such SPDEs and requires less computational operations and random variables than previously considered algorithms for simulating such SPDEs. The analysis is supported by numerical results for a stochastic heat equation, stochastic reaction diffusion equations and a stochastic Burgers equation, showing significant computational savings.
Stichworte
SDE; Stochastic differential equation; SPDE; Milstein scheme; Stochastic partial differential equation; Higher-order approximation; Numerical approximation
Erscheinungsjahr
2015
Zeitschriftentitel
Foundations of Computational Mathematics
Band
15
Ausgabe
2
Seite(n)
313-362
ISSN
1615-3375
Page URI
https://pub.uni-bielefeld.de/record/2730756

### Zitieren

Jentzen A, Röckner M. A Milstein Scheme for SPDEs. Foundations of Computational Mathematics. 2015;15(2):313-362.
Jentzen, A., & Röckner, M. (2015). A Milstein Scheme for SPDEs. Foundations of Computational Mathematics, 15(2), 313-362. doi:10.1007/s10208-015-9247-y
Jentzen, A., and Röckner, M. (2015). A Milstein Scheme for SPDEs. Foundations of Computational Mathematics 15, 313-362.
Jentzen, A., & Röckner, M., 2015. A Milstein Scheme for SPDEs. Foundations of Computational Mathematics, 15(2), p 313-362.
A. Jentzen and M. Röckner, “A Milstein Scheme for SPDEs”, Foundations of Computational Mathematics, vol. 15, 2015, pp. 313-362.
Jentzen, A., Röckner, M.: A Milstein Scheme for SPDEs. Foundations of Computational Mathematics. 15, 313-362 (2015).
Jentzen, Arnulf, and Röckner, Michael. “A Milstein Scheme for SPDEs”. Foundations of Computational Mathematics 15.2 (2015): 313-362.

Open Data PUB

### Web of Science

Dieser Datensatz im Web of Science®