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Teoriya Veroyatnostei i ee Primeneniya, 1973, Volume 18, Issue 3, Pages 605–608
(Mi tvp2734)
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This article is cited in 2 scientific papers (total in 2 papers)
Short Communications
Conditions for convergence of the superposition of stochastic processes in J-topology
D. S. Sil'vestrov Kiev
Abstract:
Let $\zeta_\varepsilon(t)$, $t\ge0$, and $\nu_\varepsilon(t)$, $t\in[0,T]$, Ьe right-continuous stochastic processes without discontinuities of the second kind.
The paper investigates conditions of convergence in J-topology of the superposition of these processes, $\zeta_\varepsilon(\nu_\varepsilon(t))$, $t\in[0,T]$.
In the case $\nu_\varepsilon(t)=t$, $t\in[0,T]$, with probability 1 these conditions coincide with well-known Skorohod's conditions of convergence of stochastic processes in J-topology.
The results obtained are applied to processes of stepped sums of a random number of random variables.
Received: 20.10.1971
Citation:
D. S. Sil'vestrov, “Conditions for convergence of the superposition of stochastic processes in J-topology”, Teor. Veroyatnost. i Primenen., 18:3 (1973), 605–608; Theory Probab. Appl., 18:3 (1974), 579–582
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https://www.mathnet.ru/eng/tvp2734 https://www.mathnet.ru/eng/tvp/v18/i3/p605
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Abstract page: | 174 | Full-text PDF : | 63 |
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