Fractional P(phi)(1)-processes and Gibbs measures
journal contributionposted on 27.05.2016 by Kamil Kaleta, Jozsef Lorinczi
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We define and prove existence of fractional P(phi)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 analyze these properties first.
- Mathematical Sciences