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

József Lőrinczi and Xiaochuan Yang

Chaos, Solitons & Fractals, 2019, vol. 120, issue C, 83-94

Abstract: We consider a class of Lévy-type processes with unbounded coefficients, arising as Doob h-transforms of Feynman-Kac type representations of non-local Schrödinger operators, where the function h is chosen to be the ground state of such an operator. First we show existence of a càdlàg 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 Hölder exponents of sample paths of ground state-transformed processes.

Keywords: Jump processes; Sample path properties; Stochastic differential equations; Hausdorff dimension; Feynman-Kac semigroups; Non-local Schrödinger operators; Ground states (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:120:y:2019:i:c:p:83-94

DOI: 10.1016/j.chaos.2019.01.008

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