Kolokoltsov, V. N. (Vasiliĭ Nikitich), Schilling, René L. and Tyukov, Alexei E.. (2004) Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Revista Matematika Iberoamerikana, Vol.20 (No.2). pp. 333-380.

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Abstract

We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present paper is to show existence, uniqueness and a (locally in time) diffeomorphism property of the solution: the solution trajectory of the system is a diffeomorphism as a function of the initial momentum. This result enables us to implement a stochastic version of the classical method of characteristics for the Hamilton-Jacobi equations. An –in itself interesting– auxiliary result are pointwise a.s. estimates for iterated stochastic integrals driven by a vector of not necessarily independent jump-type semimartingales.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Stochastic processes, Hamilton-Jacobi equations, Hamiltonian systems, Lévy processes
Journal or Publication Title:	Revista Matematika Iberoamerikana
Publisher:	Departamento de Matemáticas, Universidad Autónoma de Madrid
Date:	2004
Volume:	Vol.20
Number:	No.2
Page Range:	pp. 333-380
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Nottingham Trent University (NTU), Nuffield Foundation (NF)
Grant number:	RF175 (NTU), NAL/00056/G (NF)
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URI:	http://wrap.warwick.ac.uk/id/eprint/39372

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