Series representation of time-stable stochastic processes

Kopp, Christoph; Molchanov, Ilya (2018). Series representation of time-stable stochastic processes. Probability and mathematical statistics, 38(2), pp. 299-315. Kazimierz Urbanik Center for Probability and Mathematical Statistics 10.19195/0208-4147.38.2.4

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A stochastically continuous process ɛ(t), t­ ≥ 0, is said to be time-stable if the sum of n i.i.d. copies of ɛ equals in distribution the time-scaled stochastic process ɛ(nt), t­ ≥ 0. The paper advances the understanding of time-stable processes by means of their LePage series representations as the sum of i.i.d. processes with the arguments scaled by the sequence of successive points of the unit intensity Poisson process on [0, ∞). These series yield numerous examples of stochastic processes that share one-dimensional distributions with a Lévy process.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Molchanov, Ilya

Subjects:

500 Science > 510 Mathematics

ISSN:

0208-4147

Publisher:

Kazimierz Urbanik Center for Probability and Mathematical Statistics

Language:

English

Submitter:

Ilya Molchanov

Date Deposited:

13 Jun 2019 11:13

Last Modified:

08 Dec 2019 08:33

Publisher DOI:

10.19195/0208-4147.38.2.4

BORIS DOI:

10.7892/boris.127999

URI:

https://boris.unibe.ch/id/eprint/127999

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