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

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  • Lőrinczi, József
  • Yang, Xiaochuan

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.

Suggested Citation

  • Lőrinczi, József & Yang, Xiaochuan, 2019. "Multifractal properties of sample paths of ground state-transformed jump processes," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 83-94.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:83-94
    DOI: 10.1016/j.chaos.2019.01.008
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Xiao, Yimin, 2005. "Dimension results for sample paths of operator stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 55-75, January.
    2. Kaleta, Kamil & Lőrinczi, József, 2012. "Fractional P(ϕ)1-processes and Gibbs measures," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3580-3617.
    3. Xu, Liping, 2016. "The multifractal nature of Boltzmann processes," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2181-2210.
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