Currently displaying 1 – 5 of 5

Showing per page

Order by Relevance | Title | Year of publication

On the coupling property of Lévy processes

René L. SchillingJian Wang — 2011

Annales de l'I.H.P. Probabilités et statistiques

We give necessary and sufficient conditions guaranteeing that the coupling for Lévy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall–Rogers on couplings of random walks. In particular, we obtain that a Lévy process admits a successful coupling, if it is a strong Feller process or if the Lévy (jump) measure has an absolutely continuous component.

Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces

We introduce and systematically investigate Bessel potential spaces associated with a real-valued continuous negative definite function. These spaces can be regarded as (higher order) L p -variants of translation invariant Dirichlet spaces and in general they are not covered by known scales of function spaces. We give equivalent norm characterizations, determine the dual spaces and prove embedding theorems. Furthermore, complex interpolation spaces are calculated. Capacities are introduced and the...

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

Vassili N. Kolokol'tsovRené L. SchillingAlexei E. Tyukov — 2004

Revista Matemática Iberoamericana

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....

Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains

We use the scale of Besov spaces B τ , τ α ( ) , 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains ⊂ ℝ. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.

Page 1

Download Results (CSV)