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Fractional P(ϕ)1-processes and Gibbs measures

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  • Kaleta, Kamil
  • Lőrinczi, József
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 10 ()
    Pages: 3580-3617

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:10:p:3580-3617

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    Related research

    Keywords: Symmetric stable process; Fractional Schrödinger operator; Intrinsic ultracontractivity; Decay of ground state; Gibbs measure;

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    1. Sztonyk, Pawel, 2011. "Transition density estimates for jump Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1245-1265, June.
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