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Multifractal properties of sample paths of ground state-transformed jump processes

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journal contribution
posted on 10.01.2019, 13:48 by Jozsef Lorinczi, Xiaochuan Yang
We consider a class of Levy-type processes with unbounded coefficients, arising as Doob h-transforms of Feynman-Kac type representations of non-local Schrodinger operators, where the function h is chosen to be the ground state of such an operator. First we show existence of a cadlag version of the so-obtained ground state-transformed processes. Next we prove that they satisfy a related stochastic differential equation with jumps. Making use of this SDE, we then derive and prove the multifractal spectrum of local Holder exponents of sample paths of ground state-transformed processes.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Chaos, Solitons and Fractals

Citation

LORINCZI, J. and YANG, X., 2019. Multifractal properties of sample paths of ground state-transformed jump processes. Chaos, Solitons and Fractals, 120, pp.83-94.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This paper was accepted for publication in the journal Chaos, Solitons and Fractals and the definitive published version is available at https://doi.org/10.1016/j.chaos.2019.01.008.

Acceptance date

09/01/2019

Publication date

2019-01-31

ISSN

0960-0779

Language

en

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