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Mat. Sb. (N.S.), 1981, Volume 116(158), Number 3(11), Pages 331–358 (Mi msb2471)  

This article is cited in 7 scientific papers (total in 8 papers)

On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments

R. Sh. Liptser, A. N. Shiryaev


Abstract: The authors study weak convergence of a sequence of semimartingales to an arbitrary stochastically continuous process independent or conditionally independent increments. The “semimartingale scheme” they consider includes the traditional “series scheme”.
Bibliography: 22 titles.

Full text: PDF file (1928 kB)
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English version:
Mathematics of the USSR-Sbornik, 1983, 44:3, 299–323

Bibliographic databases:

UDC: 519.2
MSC: Primary 60F05, 60G17, 60G48; Secondary 46E27, 60G15, 60G25, 60J30
Received: 09.02.1981

Citation: R. Sh. Liptser, A. N. Shiryaev, “On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments”, Mat. Sb. (N.S.), 116(158):3(11) (1981), 331–358; Math. USSR-Sb., 44:3 (1983), 299–323

Citation in format AMSBIB
\Bibitem{LipShi81}
\by R.~Sh.~Liptser, A.~N.~Shiryaev
\paper On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 3(11)
\pages 331--358
\mathnet{http://mi.mathnet.ru/msb2471}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=665687}
\zmath{https://zbmath.org/?q=an:0505.60035|0484.60024}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 3
\pages 299--323
\crossref{https://doi.org/10.1070/SM1983v044n03ABEH000969}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. I. Grigelionis, K. Kubilyus, R. A. Mikulyavichyus, “The martingale approach to functional limit theorems”, Russian Math. Surveys, 37:6 (1982), 41–54  mathnet  crossref  mathscinet  zmath  isi
    2. V. V. Lavrent'ev, “On the weak convergence of Hilbert space-valued semimartingales to stochastically continuous processes with conditionally independent increments”, Russian Math. Surveys, 38:3 (1983), 149–150  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. R. Sh. Liptser, A. N. Shiryaev, “Weak convergence of a sequence of semimartingales to a process of diffusion type”, Math. USSR-Sb., 49:1 (1984), 171–195  mathnet  crossref  mathscinet  zmath
    4. Grigelionis B., Mikulevicius R., “On Contiguity and Weak-Convergence of Probability-Measures”, 1021, 1983, 177–194  mathscinet  zmath  isi
    5. A. F. Taraskin, “On the limiting behaviour of the likelihood ratio for semimartingales”, Russian Math. Surveys, 40:2 (1985), 237–238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. E. Mordecki, “Necessary Conditions for Stable Convergenceof Semimartingales”, Theory Probab Appl, 44:1 (2000), 217  mathnet  crossref  mathscinet  isi
    7. V. V. Lavrentev, A. L. Bugrimov, “Usloviya kompaktnosti semeistva mer gilbertovoznachnykh nepreryvnykh semimartingalov”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2019, no. 4, 39–51  mathnet  crossref  elib
    8. V. M. Abramov, B. M. Miller, E. Ya. Rubinovich, P. Yu. Chiganskii, “Razvitie teorii stokhasticheskogo upravleniya i filtratsii v rabotakh R. Sh. Liptsera”, Avtomat. i telemekh., 2020, no. 3, 3–13  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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