Geodesic
Weak convergence of Hilbert-valued semimartingales to a stochastically continuous process with independent increments
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2024), pp. 5-16

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The paper studies the weak convergence of semimartingales taking values in Hilbert space to an arbitrary stochastically continuous process with independent increments. Sufficient conditions for the weak convergence of such semimartingales to a stochastically continuous semimartingale with independent increments are obtained.
Keywords: semimartingale, Hilbert space, weak convergence, stochastically continuous processes. 
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     author = {V. V. Lavrentyev},
     title = {Weak convergence of {Hilbert-valued} semimartingales to a stochastically continuous process with independent increments},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
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     publisher = {mathdoc},
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     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/VTPMK_2024_1_a0/}
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V. V. Lavrentyev. Weak convergence of Hilbert-valued semimartingales to a stochastically continuous process with independent increments. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2024), pp. 5-16. http://geodesic.mathdoc.fr/item/VTPMK_2024_1_a0/