Minimal Errors for Strong and Weak Approximation of Stochastic Differential Equations

Thomas Müller-Gronbach () and Klaus Ritter ()
Additional contact information
Thomas Müller-Gronbach: Fern Universität Hagen, Fakultät für Mathematik und Informatik
Klaus Ritter: Technische Universität Darmstadt, Fachbereich Mathematik

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 53-82 from Springer

Abstract: Summary We present a survey of results on minimal errors and optimality of algorithms for strong and weak approximation of systems of stochastic differential equations. For strong approximation, emphasis lies on the analysis of algorithms that are based on point evaluations of the driving Brownian motion and on the impact of non-commutativity, if present. Furthermore, we relate strong approximation to weighted integration and reconstruction of Brownian motion, and we demonstrate that the analysis of minimal errors leads to new algorithms that perform asymptotically optimal. In particular, these algorithms use a path-dependent step-size control. for weak approximation we consider the problem of computing the expected value of a functional of the solution, and we concentrate on recent results for a worst-case analysis either with respect to the functional or with respect to the coefficients of the system. Moreover, we relate weak approximation problems to average Kolmogorov widths and quantization numbers as well as to high-dimensional tensor product problems.

Keywords: Brownian Motion; Minimal Error; Fractional Brownian Motion; Deterministic Algorithm; Euler Scheme (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_4

Ordering information: This item can be ordered from
http://www.springer.com/9783540744962

DOI: 10.1007/978-3-540-74496-2_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().