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Non-standard Skorokhod convergence of Levy-driven convolution integrals in Hilbert spaces

Research output: Contribution to journalArticlepeer-review

Ilya Pavlyukevich, Markus Riedle

Original languageEnglish
Pages (from-to)271-305
Number of pages35
JournalSTOCHASTIC ANALYSIS AND APPLICATIONS
Volume33
Issue number2
Early online date2 Feb 2015
DOIs
Accepted/In press12 Nov 2014
E-pub ahead of print2 Feb 2015
Published2015

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Abstract

We study the convergence in probability in the non-standard M1 Skorokhod topology of the Hilbert valued stochastic convolution integrals of the type ∫Fγ(t−s)dL(s) to a process ∫F(t−s)dL(s) driven by a Lévy process L. In Banach spaces we introduce strong, weak and product modes of M1-convergence, prove a criterion for the M1-convergence in probability of stochastically continuous càdlàg processes in terms of the convergence in probability of the finite dimensional marginals and a good behaviour of the corresponding oscillation functions, and establish criteria for the convergence in probability of Lévy driven stochastic convolutions. The theory is applied to the infinitely dimensional integrated Ornstein-Uhlenbeck processes with diagonalisable generators.

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