Series representation of time-stable stochastic processes

• Autorzy: Kopp C. , Molchanov I.

Identyfikatory

DOI

10.19195/0208-4147.38.2.4

• Języki publikacji: EN

Abstrakty

EN

A stochastically continuous process ξ(t), t ≥ 0, is said to be time-stable if the sum of n i.i.d. copies of ξ equals in distribution the time-scaled stochastic process ξ(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.

Słowa kluczowe

EN

infinite divisibility; LePage series; Lévy process; point process; time-stable process

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2018
• Tom: Vol. 38, Fasc. 2
• Strony: 299--315
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Kopp C.

• School of Agricultural, Forest and Food Sciences, Bern University of Applied Sciences, Länggasse 85, CH-3052 Zollikofen, Switzerland

autor

Molchanov I.

• Institute of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).