Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations.

Kolokol'tsov, Vassili N., Schilling, René L., and Tyukov, Alexei E.. "Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations.." Revista Matemática Iberoamericana 20.2 (2004): 333-380. <http://eudml.org/doc/39720>.

@article{Kolokoltsov2004,
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 papel 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.},
author = {Kolokol'tsov, Vassili N., Schilling, René L., Tyukov, Alexei E.},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones diferenciales estocásticas; Integración estocástica; Ecuación de Hamilton-Jacobi; Lévy noise; well-posedness; method of characteristics},
language = {eng},
number = {2},
pages = {333-380},
title = {Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations.},
url = {http://eudml.org/doc/39720},
volume = {20},
year = {2004},
}

TY - JOUR
AU - Kolokol'tsov, Vassili N.
AU - Schilling, René L.
AU - Tyukov, Alexei E.
TI - Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations.
JO - Revista Matemática Iberoamericana
PY - 2004
VL - 20
IS - 2
SP - 333
EP - 380
AB - We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present papel 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.
LA - eng
KW - Ecuaciones diferenciales estocásticas; Integración estocástica; Ecuación de Hamilton-Jacobi; Lévy noise; well-posedness; method of characteristics
UR - http://eudml.org/doc/39720
ER -