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Time Change Equations for Lévy Type Processes

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.

preprint2015arXivOpen access
Paul KrühnerAlexander Schnurr
math.PR
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Open access2 authors1 topic
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Paul KrühnerAlexander Schnurr

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