January 2022 The suprema of infinitely divisible processes
Witold Bednorz, Rafał Martynek
Author Affiliations +
Ann. Probab. 50(1): 397-417 (January 2022). DOI: 10.1214/21-AOP1546


In this paper we complete the full characterization of the expected suprema of infinitely divisible processes. In particular, we remove the technical assumption called H(C0,δ) condition and settle positively the conjecture posed by M. Talagrand.

Funding Statement

The first author was supported by NCN Grant UMO-2016/21/B/ST1/01489. The second author was supported by NCN Grant UMO-2018/31/N/ST1/03982.


The authors would like to thank Professor Michel Talagrand for the most helpful comments and suggestions on the whole approach to the problem, especially for pointing out that proofs of steps (5) and (4) are possible in their present form.

Also, we are very grateful to the anonymous referees for suggesting substantial changes of the exposition of the material in the paper which made it significantly clearer and more readable as well as for pointing out numerous errors in the initial version of the paper.


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Witold Bednorz. Rafał Martynek. "The suprema of infinitely divisible processes." Ann. Probab. 50 (1) 397 - 417, January 2022. https://doi.org/10.1214/21-AOP1546


Received: 1 May 2020; Revised: 1 August 2021; Published: January 2022
First available in Project Euclid: 23 February 2022

MathSciNet: MR4385829
zbMATH: 1498.60146
Digital Object Identifier: 10.1214/21-AOP1546

Primary: 60G15 , 60G17

Keywords: Bernoulli process , infinitely divisible processes , Lévy measure , process boundedness , Rosiński representation

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 1 • January 2022
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