Time Change Equations for Lévy Type Processes

2015/08/10 by Krühner, Paul, Schnurr, Alexander
#45G10 #60G17 #60J75 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1508.02235

Abstract

In this paper we analyse time change equations (TCEs) for Lévy-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 Lévy-type processes found in Schnurr (2013). Applications include an existence result for processes which correspond to a certain class of given symbols.

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