Let us assume that (S,S) is a metric space with Borel σ algebra S and η̃ is a time homogeneous compensated Poisson randommeasure defined on a filtered probability space (Ω;F ; (Ft)0≤t<∞;P) with intensity measure ν on S, to be specified later. Let us assume that 1 < p ≤ 2, E is a Banach space of martingale type p, see e.g. the Appendix of [7] for a definition. We consider in the following the Itô...

Abstract We use a Voronoi-type tessellation based on compound Poisson point process to construct polynomially mixing stationary random smooth planar vector field with bounded nonnegative components such that, probability one, none of the associated integral curves possess an asymptotic direction.

In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.

This paper is concerned with the implementation and investigation of integral equation based solvers as preconditioners for nite diierence discretizations of Poisson equations in geometrically complex domains. The target discretizations are those associated with \cut-out" grids. We discuss such grids and also describe a software structure which enables their rapid construction. Computational re...

We prove the existence of axially symmetric solutions to the Vlasov– Poisson system in a rotating setting for sufficiently small angular velocity. The constructed steady states depend on Jacobi’s integral and the proof relies on an implicit function theorem for operators.

A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional excursions. Mathematics Subject Classification (2000): Primary 60J80; Secondary 60G57, 60H20

We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a Brownian part as well as a pure jump part. We state an annealed convergence theorem. This problem is deeply connected with homogenization of integral partial diff...

This is the first in a series of papers dedicated to the study of Poisson manifolds of compact types (PMCTs). This notion encompasses several classes of Poisson manifolds defined via properties of their symplectic integrations. In this first paper we establish some fundamental properties and constructions of PMCTs. For instance, we show that their Poisson cohomology behaves very much like the d...

This note describes the functional-integral quantization of two-dimensional topological field theories together with applications to problems in deformation quantization of Poisson manifolds and reduction of certain submanifolds. A brief introduction to smooth graded manifolds and to the Batalin–Vilkovisky formalism is included. Mathematics Subject Classification (2000). Primary 81T45; Secondar...

Ġ = {G,H}. In particular, the DV F is called an integral if it has zero PB with the Hamiltonian {F,H} = 0. In this case F does not depend on t. In many problems of the classical mechanics DV form elegant algebraic structures which are closed with respect to PB. The Poisson structures with non-linear PB were discussed in [9] and [6]. Sklyanin introduced [9] the so-called quadratic Poisson algebr...