Kaleta, Kamil Lorinczi, Jozsef Fractional P(phi)(1)-processes and Gibbs measures 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. Symmetric stable process;Fractional Schrodinger operator;Intrinsic ultracontractivity;Decay of ground state;Gibbs measure;Statistics;Mathematical Sciences not elsewhere classified 2016-05-27
    https://repository.lboro.ac.uk/articles/journal_contribution/Fractional_P_phi_1_-processes_and_Gibbs_measures/9389087