Multifractal properties of sample paths of ground state-transformed jump processes
journal contributionposted 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.
- Mathematical Sciences