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Generalization of the Blumenthal-Getoor index to the class of homogeneous diffusions with jumps and some applications. (English) Zbl 1301.60092
The ‘symbol’ of a process is defined as the state-dependent right derivative at \(t = 0\) of the characteristic function and is used in turn to define four ‘indices at the origin’ and four ‘indices at infinity’ for the process. The main result is a characterization of sample path asymptotics for homogeneous diffusions as time tends to zero, resp. infinity, in terms of these indices. Examples and related results are provided. A separate contribution is a construction of a homogeneous diffusion that is not Markov.

MSC:
60J60 Diffusion processes
60G17 Sample path properties
60J25 Continuous-time Markov processes on general state spaces
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