Change of variable formulas for non-anticipative functionals on path
space
space
File(s)1004.1380v1.pdf (312.37 KB)
Accepted version
Author(s)
Cont, R
Fournie, D-A
Type
Journal Article
Abstract
We derive a functional change of variable formula for non-anticipative
functionals defined on the space of right continuous paths with left limits.
The functional is only required to possess certain directional derivatives,
which may be computed pathwise. Our results lead to functional extensions of
the Ito formula for a large class of stochastic processes, including
semimartingales and Dirichlet processes. In particular, we show the stability
of the class of semimartingales under certain functional transformations.
functionals defined on the space of right continuous paths with left limits.
The functional is only required to possess certain directional derivatives,
which may be computed pathwise. Our results lead to functional extensions of
the Ito formula for a large class of stochastic processes, including
semimartingales and Dirichlet processes. In particular, we show the stability
of the class of semimartingales under certain functional transformations.
Date Issued
2010-04-08
Citation
Journal of Functional Analysis, 2010, 259, pp.1043-1072
ISSN
0022-1236
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Start Page
1043
End Page
1072
Journal / Book Title
Journal of Functional Analysis
Volume
259
Issue
4
Copyright Statement
© 2010 Elsevier Inc. All rights reserved. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in JOURNAL OF FUNCTIONAL ANALYSIS, [Vol:259, Issue:4, (2010)] DOI: http://dx.doi.org/10.1016/j.jfa.2010.04.017
Description
20.02.13 KB. Elsevier says okd for accepted version ok to add while mandate not enforced. Elsevier
Identifier
http://arxiv.org/abs/1004.1380v1
Subjects
change of variable formula, functional derivative, functional calculus, stochastic integral, stochastic calculus, quadratic variation, Ito formula, Dirichlet process, semimartingale, Wiener space, Follmer integral, Ito integral, cadlag functions.