Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains

Intrinsic Ultracontractivity, Conditional Lifetimes and Conditional Gauge for Symmetric Stable Processes on Rough Domains

For a symmetric α-stable process X on Rn with 0 < α < 2, n ≥ 2 and a domain D ⊂ Rn, let LD be the infinitesimal generator of the subprocess ofX killed upon leaving D. For a Kato class function q, it is shown that LD + q is intrinsic ultracontractive on a Hölder domain D of order 0. This is then used to establish the conditional gauge theorem for X on bounded Lipschitz domains in Rn. It is also ...

Intrinsic Ultracontractivity for Non-symmetric Lévy Processes

Recently in [17, 18], we extended the concept of intrinsic ultracontractivity to nonsymmetric semigroups and proved that for a large class of non-symmetric diffusions Z with measure-valued drift and potential, the semigroup of ZD (the process obtained by killing Z upon exiting D) in a bounded domain is intrinsic ultracontractive under very mild assumptions. In this paper, we study the intrinsic...

Intrinsic Ultracontractivity of Non-symmetric Diffusion Semigroups in Bounded Domains

We extend the concept of intrinsic ultracontractivity to non-symmetric semigroups and prove the intrinsic ultracontractivity of the Dirichlet semigroups of nonsymmetric second order elliptic operators in bounded Lipschitz domains.

General Gauge and Conditional Gauge

On Testing the Adequacy of Stable Processes under Conditional Heteroscedasticity

We consider a recently proposed method of estimating the tail index and testing the goodness-of-fit of dependent stable processes. Through Monte Carlo simulations, we evaluate the ability of the procedure to distinguish between stable and non-stable processes in the presence of non-linear dependence and to estimate the tail index of the distribution. We then apply the test to black market East ...