Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations.
Boundary-value problems for Hamiltonian systems and absolute minimizers in calculus of variations.
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations.
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....
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