Multifractal properties of sample paths of ground state-transformed jump processes
Jozsef Lorinczi
Xiaochuan Yang
2134/36534
https://repository.lboro.ac.uk/articles/journal_contribution/Multifractal_properties_of_sample_paths_of_ground_state-transformed_jump_processes/9376802
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.
2019-01-10 13:48:30
Jump processes
Sample path properties
Stochastic differential equations
Hausdorff dimension
Feynman-Kac semigroups
Non-local Schrodinger operators
Ground states
Mathematical Sciences not elsewhere classified