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November 2018 Multifractality of jump diffusion processes
Xiaochuan Yang
Ann. Inst. H. Poincaré Probab. Statist. 54(4): 2042-2074 (November 2018). DOI: 10.1214/17-AIHP864

Abstract

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.

Nous étudions la régularité locale et la nature multifractale des trajectoires de diffusion à sauts, qui sont solutions d’une classe d’équations stochastiques à sauts. Cet article prolonge et étend substantiellement le travail récent de Barral et al. qui ont construit un processus de Markov de sauts purs avec un spectre multifractal aléatoire. La classe considérée est beaucoup plus large et présente de nouveaux phénomènes multifractals notamment sur les valeurs extrêmes du spectre. Cette classe comprend les processus de type stable au sens de Bass et des EDS non dégénérées guidées par un processus stable.

Citation

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Xiaochuan Yang. "Multifractality of jump diffusion processes." Ann. Inst. H. Poincaré Probab. Statist. 54 (4) 2042 - 2074, November 2018. https://doi.org/10.1214/17-AIHP864

Information

Received: 9 October 2015; Revised: 17 August 2017; Accepted: 4 September 2017; Published: November 2018
First available in Project Euclid: 18 October 2018

zbMATH: 06996558
MathSciNet: MR3865666
Digital Object Identifier: 10.1214/17-AIHP864

Subjects:
Primary: 28A78, 28A80, 60H10, 60J25, 60J75

Rights: Copyright © 2018 Institut Henri Poincaré

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Vol.54 • No. 4 • November 2018
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