A basis for iterated stochastic integrals

J.G. Gaines

Mathematics and Computers in Simulation (MATCOM), 1995, vol. 38, issue 1, 7-11

Abstract: We explore the algebra of the sets of iterated Stratonovich or Ito integrals that appear in the stochastic Taylor series expansion of the solution to a stochastic differential equation. The algebra of iterated Stratonovich integrals with pointwise multiplication is a shuffle algebra, allowing us to apply results from work on shuffle algebras. The pointwise product of Ito integrals is a modified shuffle product. Lyndon words provide an algebraic basis for both sets of iterated integrals. This basis is similar to, but simpler than, that obtained by Sussmann using Hall words.

Date: 1995
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378475493E00619
Full text for ScienceDirect subscribers only

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:eee:matcom:v:38:y:1995:i:1:p:7-11

DOI: 10.1016/0378-4754(93)E0061-9

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().