Open Access
June, 2004 Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations
Vassili N. Kolokol'tsov, René L. Schilling, Alexei E. Tyukov
Rev. Mat. Iberoamericana 20(2): 333-380 (June, 2004).


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 impulse. 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.


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Vassili N. Kolokol'tsov. René L. Schilling. Alexei E. Tyukov. "Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations." Rev. Mat. Iberoamericana 20 (2) 333 - 380, June, 2004.


Published: June, 2004
First available in Project Euclid: 17 June 2004

zbMATH: 1060.70025
MathSciNet: MR2073123

Primary: 60H05 , 60H15 , 70H20
Secondary: 60G51 , 60J75 , 70H05

Keywords: Hamiltonian system , iterated stochastic integral , Lévy process , method of stochastic characteristics , Semimartingale , stochastic Hamilton-Jacobi equation

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.20 • No. 2 • June, 2004
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