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In this paper we analyse time change equations (TCEs) for L\'evy-typeprocesses in detail. To this end we establish a connection between TCEs andclassical one-dimensional initial value problems (IVPs) which are easier tohandle. Properties of the IVPs are linked with properties of the TCEs. We showin a general setting existence and uniqueness of solutions of the TCEs. Ourmain result is based on the general path properties for L\'evy-type processesfound in Schnurr (2013). Applications include an existence result for processeswhich correspond to a certain class of given symbols.

Time Change Equations for L\'evy Type Processes