KALETA, K. and LORINCZI, J., 2012. Fractional P(phi)(1)-processes and Gibbs measures. Stochastic Processes and their Applications, 122(10), pp. 3580-3617.
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.
This paper was accepted for publication in the journal Stochastic Processes and their Applications and the definitive published version is available at http://dx.doi.org/10.1016/j.spa.2012.06.001