Iterated Logarithm Law for Anticipating Stochastic Differential Equations

David Márquez-Carreras () and Carles Rovira ()
Additional contact information
David Márquez-Carreras: Universitat de Barcelona
Carles Rovira: Universitat de Barcelona

Journal of Theoretical Probability, 2008, vol. 21, issue 3, 650-659

Abstract: Abstract We prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations $$\xi^{u}_{t}=X_{0}^{u}+\frac{1}{\sqrt{\log\log u}}\sum_{j=1}^{k}\int_{0}^{t}A_{j}^{u}(\xi^{u}_{s})\circ dW_{s}^{j}+\int_{0}^{t}A_{0}^{u}(\xi^{u}_{s})ds,$$ where u>e, W={(W t 1 ,…,W t k ),0≤t≤1} is a standard k-dimensional Wiener process, $A_{0}^{u},A_{1}^{u},\dots,A_{k}^{u}:\mathbb{R}^{d}\longrightarrow \mathbb{R}^{d}$ are functions of class $\mathcal{C}^{2}$ with bounded partial derivatives up to order 2, X 0 u is a random vector not necessarily adapted and the first integral is a generalized Stratonovich integral.

Keywords: Iterated logarithm law; Stochastic differential equations; Anticipative calculus; 60H10; 60H15 (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-007-0114-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:jotpro:v:21:y:2008:i:3:d:10.1007_s10959-007-0114-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-007-0114-x

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().