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Criteria for the Finiteness of the Strong $p$-Variation for Lévy-type Processes

Using generalized Blumenthal--Getoor indices, we obtain criteria for the finiteness of the $p$-variation of Lévy-type processes. This class of stochastic processes includes solutions of Skorokhod-type stochastic differential equations (SDEs), certain Feller processes and solutions of Lévy driven SDEs. The class of processes is wider than in earlier contributions and using fine continuity we are able to handle general measurable subsets of $R^d$ as state spaces. Furthermore, in contrast to previous contributions on the subject, we introduce a local index in order to complement the upper index. This local index yields a sufficient condition for the infiniteness of the $p$-variation. We discuss various examples in order to demonstrate the applicability of the method.