Fractional P(ϕ)1-processes and Gibbs measures

Kamil Kaleta and József Lőrinczi

Stochastic Processes and their Applications, 2012, vol. 122, issue 10, 3580-3617

Abstract: We define and prove existence of fractional P(ϕ)1-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 analyse these properties first.

Keywords: Symmetric stable process; Fractional Schrödinger operator; Intrinsic ultracontractivity; Decay of ground state; Gibbs measure (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:10:p:3580-3617

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DOI: 10.1016/j.spa.2012.06.001

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