On Poisson integrals

Nonabsolutely convergent Poisson integrals

If a function f has finite Henstock integral on the boundary of the unit disk of R 2 then its Poisson integral exists for |z| < 1 and is o((1 − |z|) −1) as |z| → 1 −. It is shown that this is the best possible uniform pointwise estimate. For an L 1 measure the best estimate is O((1 − |z|) −1). In this paper we consider estimates of Poisson integrals on the unit circle with respect to Alexiewicz...

Anticipating integrals and martingales on the Poisson space

Let Ñt be a standard compensated Poisson process on [0, 1]. We prove a new characterization of anticipating integrals of the Skorohod type with respect to Ñ , and use it to obtain several counterparts to well established properties of semimartingale stochastic integrals. In particular we show that, if the integrand is sufficiently regular, anticipating Skorohod integral processes with respect t...

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

Central limit theorems for double Poisson integrals

Motivated by second order asymptotic results, we characterize the convergence in law of double integrals, with respect to Poisson random measures, toward a standard Gaussian distribution. Our conditions are expressed in terms of contractions of the kernels. To prove our main results, we use the theory of stable convergence of generalized stochastic integrals developed by Peccati and Taqqu. One ...

Convergence of poisson integrals for bounded symmetric domains.

1. The purpose of this note is to describe the extension of the almost everywhere convergence of Poisson integrals to the case of the bounded symmetric domains of Cartan. It is useful to realize such a bounded symmetric domain D as a generalized upper half-plane (i.e., a Siegel domain of type II), and this is done as follows. Let V1 and V2 be two finite-dimensional vector spaces over C. Assume ...