Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations
Kolokol'tsov, Vassili N. ; Schilling, René L. ; Tyukov, Alexei E.
Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, p. 333-380 / Harvested from Project Euclid
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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.
Publié le : 2004-06-14
Classification:  stochastic Hamilton-Jacobi equation,  Hamiltonian system,  method of stochastic characteristics,  iterated stochastic integral,  semimartingale,  Lévy process,  70H20,  60H15,  60H05,  60G51,  60J75,  70H05 
@article{1087482018,
     author = {Kolokol'tsov, Vassili N. and Schilling, Ren\'e L. and Tyukov, Alexei E.},
     title = {Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations},
     journal = {Rev. Mat. Iberoamericana},
     volume = {20},
     number = {1},
     year = {2004},
     pages = { 333-380},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087482018}
}

Kolokol'tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E. Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp.  333-380. http://gdmltest.u-ga.fr/item/1087482018/