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- W4300187938 abstract "We study the convergence in probability in the non-standard $M_1$ Skorokhod topology of the Hilbert valued stochastic convolution integrals of the type $int_0^t F_gamma(t-s),d L(s)$ to a process $int_0^t F(t-s), d L(s)$ driven by a L'evy process $L$. In Banach spaces we introduce strong, weak and product modes of $M_1$-convergence, prove a criterion for the $M_1$-convergence in probability of stochastically continuous c`adl`ag 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 L'evy driven stochastic convolutions. The theory is applied to the infinitely dimensional integrated Ornstein--Uhlenbeck processes with diagonalisable generators." @default.
- W4300187938 created "2022-10-03" @default.
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- W4300187938 date "2013-11-06" @default.
- W4300187938 modified "2023-10-17" @default.
- W4300187938 title "Non-standard Skorokhod convergence of Levy-driven convolution integrals in Hilbert spaces" @default.
- W4300187938 doi "https://doi.org/10.48550/arxiv.1311.1342" @default.
- W4300187938 hasPublicationYear "2013" @default.
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