Time Change Equations for L\'evy Type Processes
Probability
2015-08-11 v1
Abstract
In this paper we analyse time change equations (TCEs) for L\'evy-type processes in detail. To this end we establish a connection between TCEs and classical one-dimensional initial value problems (IVPs) which are easier to handle. Properties of the IVPs are linked with properties of the TCEs. We show in a general setting existence and uniqueness of solutions of the TCEs. Our main result is based on the general path properties for L\'evy-type processes found in Schnurr (2013). Applications include an existence result for processes which correspond to a certain class of given symbols.
Keywords
Cite
@article{arxiv.1508.02235,
title = {Time Change Equations for L\'evy Type Processes},
author = {Paul Krühner and Alexander Schnurr},
journal= {arXiv preprint arXiv:1508.02235},
year = {2015}
}