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Multifractality of jump diffusion processes. (English. French summary) Zbl 1417.60074

Summary: We study the local regularity and multifractal nature of the sample paths of jump diffusion processes, which are solutions to a class of stochastic differential equations with jumps. This article extends the recent work of Barral et al. who constructed a pure jump monotone Markov process with random multifractal spectrum. The class of processes studied here is much larger and exhibits novel features on the extreme values of the spectrum. This class includes Bass’ stable-like processes and non-degenerate stable-driven SDEs.

MSC:

60J75 Jump processes (MSC2010)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J25 Continuous-time Markov processes on general state spaces
28A80 Fractals
28A78 Hausdorff and packing measures
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