ON ESTIMATES OF POISSON KERNELS FOR SYMMETRIC LÉVY PROCESSES

Estimates on Green functions and Poisson kernels for symmetric stable processes

One of the most basic and most important subfamily of Lévy processes is symmetric stable processes. A symmetric α-stable process X on Rn is a Lévy process whose transition density p(t , x − y) relative to the Lebesgue measure is uniquely determined by its Fourier transform ∫ Rn e ix ·ξp(t , x )dx = e−t|ξ| α . Here α must be in the interval (0, 2]. When α = 2, we get a Brownian motion running wi...

Gaussian estimates for symmetric simple exclusion processes

2014 We prove Gaussian tail estimates for the transition probability of n particles evolving as symmetric exclusion processes on Zd, improving results obtained in [9]. We derive from this result a non-equilibrium Boltzmann-Gibbs principle for the symmetric simple exclusion process in dimension 1 starting from a product measure with slowly varying parameter. RÉSUMÉ. 2014 We prove Gaussian tail e...

Estimates for Derivatives of the Poisson Kernels on Homogeneous Manifolds of Negative Curvature

We obtain estimates for derivatives of the Poisson kernels for the second order differential operators on homogeneous manifolds of negative curvature both in the coercive and noncoercive case.

Reproducing kernels , Bergman kernels , Poisson kernels

Exact Statistical Inference for Some Parametric Nonhomogeneous Poisson Processes

Nonhomogeneous Poisson processes (NHPPs) are often used to model recurrent events, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for certain parametric NHPPs, using a method based on Monte Carlo simulation conditional on sufficient statistics. A closely related way of obtaining exact confidence intervals in parametri...