Fractional -processes and Gibbs measures
arXiv:1011.2713 · doi:10.1016/j.spa.2012.06.001
Abstract
We define and prove existence of fractional -processes as random processes generated by fractional Schrödinger semigroups with Kato-decomposable potentials. Also, we show that the measure of such a process is a Gibbs measure with respect to the same potential. We give conditions of its uniqueness and characterize its support relating this with intrinsic ultracontractivity properties of the semigroup and the fall-off of the ground state. To achieve that we establish and analyze these properties first.
37 pages
References in corpus (5)
- Markovian bridges: Weak continuity and pathwise constructions
- Lieb-Thirring Bound for Schrödinger Operators with Bernstein Functions of the Laplacian
- Functional Integral Representation of the Pauli-Fierz Model with Spin 1/2
- Probabilistic Representation and Fall-Off of Bound States of Relativistic Schrödinger Operators with Spin 1/2
- Spectral Properties of the Massless Relativistic Harmonic Oscillator
Cited by in corpus (8)
- Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of Lévy processes
- Fall-off of eigenfunctions for non-local Schrödinger operators with decaying potentials
- Orbital-free density functional theory of out-of-plane charge screening in graphene
- Transition in the decay rates of stationary distributions of Lévy motion in an energy landscape
- Multifractal properties of sample paths of ground state-transformed jump processes
- Heat content and small time asymptotics for Schrödinger operators on
- Law of large numbers for branching symmetric Hunt processes with measure-valued branching rates
- Heat content estimates for the fractional Schrödinger operator $\F+\ind$