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

## TL;DR

This paper studies the multifractal properties of sample paths of ground state-transformed jump processes derived from non-local Schr"odinger operators, establishing their existence, SDE characterization, and multifractal spectrum.

## Contribution

It introduces a new class of jump processes from ground state transformations and characterizes their multifractal spectrum, extending understanding of their path regularity.

## Key findings

- Existence of cadlag version of the processes
- Representation via stochastic differential equations with jumps
- Derivation of the multifractal spectrum of sample paths

## Abstract

We consider a class of L\'evy-type processes with unbounded coefficients, arising as Doob $h$-transforms of Feynman-Kac type representations of non-local Schr\"odinger operators, where the function $h$ is chosen to be the ground state of such an operator. First, we show the existence of a c\`adl\`ag 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 H\"older exponents of sample paths of ground state-transformed processes.