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Fractional P(phi)(1)-processes and Gibbs measures

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journal contribution
posted on 27.05.2016 by Kamil Kaleta, Jozsef Lorinczi
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Volume

122

Issue

10

Pages

3580 - 3617 (38)

Citation

KALETA, K. and LORINCZI, J., 2012. Fractional P(phi)(1)-processes and Gibbs measures. Stochastic Processes and their Applications, 122(10), pp. 3580-3617.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2012

Notes

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

ISSN

0304-4149

Language

en

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