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Time change equations for Lévy-type processes. (English) Zbl 1382.60110
Summary: We consider time change equations for Lévy-type processes. In this context we generalize the results of B. Böttcher et al. [Lévy matters III. Lévy-type processes: construction, approximation and sample path properties. Cham: Springer (2013; Zbl 1384.60004)] significantly. Namely, we are able to incorporate measurable instead of continuous multipliers. This opens a gate to find whole classes of symbols for which corresponding processes do exist. In order to establish our results we carefully analyze the connection between time change equations and classical initial value problems. This relationship allows us to transfer well-known results from this classical subject of pure mathematics into the theory of stochastic processes. On the way to prove our main theorem we establish generalizations of results on paths of Lévy-type processes.

60J75 Jump processes (MSC2010)
45G10 Other nonlinear integral equations
60G17 Sample path properties
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