Asymptotic expansion of resolvent kernels and behavior of spectral functions for symmetric stable processes

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

asymptotic behavior of multivariate reward processes with nonlinear reward functions

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...

The Asymptotic Expansion of Spherical Functions on Symmetric Cones

In [7], Genkai Zhang gives the asymptotic expansion for the spherical functions on symmetric cones. This is done to prove a central limit theorem for these spaces. The work of Zhang is a natural continuation of the work of Audrey Terras [6] (the case of the positive definite matrices of rank 2) and of the work of Donald St.P. Richards [3] (the case of the positive definite matrices of all ranks...

Analytic Continuation of Resolvent Kernels on Noncompact Symmetric Spaces

Let X = G/K be a symmetric space of noncompact type and let ∆ be the Laplacian associated with a G-invariant metric on X . We show that the resolvent kernel of ∆ admits a holomorphic extension to a Riemann surface depending on the rank of the symmetric space. This Riemann surface is a branched cover of the complex plane with a certain part of the real axis removed. It has a branching point at t...