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Title: Multifractal properties of sample paths of ground state-transformed jump processes
Authors: Lorinczi, Jozsef
Yang, Xiaochuan
Keywords: Jump processes
Sample path properties
Stochastic differential equations
Hausdorff dimension
Feynman-Kac semigroups
Non-local Schrodinger operators
Ground states
Issue Date: 2019
Publisher: Elsevier
Citation: LORINCZI, J. and YANG, X., 2019. Multifractal properties of sample paths of ground state-transformed jump processes. Chaos, Solitons and Fractals, [in press].
Abstract: 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.
Description: This paper is closed access until 12 months after the date of publication.
Sponsor: JL thanks IHES, Bures-sur-Yvette, for a visiting fellowship, where part of this paper has been written.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/36534
Publisher Link: https://www.journals.elsevier.com/chaos-solitons-and-fractals
ISSN: 0960-0779
Appears in Collections:Closed Access (Maths)

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