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.
Citation:
R. Sh. Liptser, A. N. Shiryaev, “On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments”, Math. USSR-Sb., 44:3 (1983), 299–323
\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 Math. USSR-Sb.
\yr 1983
\vol 44
\issue 3
\pages 299--323
\mathnet{http://mi.mathnet.ru/eng/sm2471}
\crossref{https://doi.org/10.1070/SM1983v044n03ABEH000969}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=665687}
\zmath{https://zbmath.org/?q=an:0505.60035|0484.60024}
Linking options:
https://www.mathnet.ru/eng/sm2471
https://doi.org/10.1070/SM1983v044n03ABEH000969
https://www.mathnet.ru/eng/sm/v158/i3/p331
This publication is cited in the following 10 articles:
S. O. Sharipov, “Funktsionalnaya predelnaya teorema dlya kriticheskogo vetvyaschegosya protsessa so slabo zavisimoi immigratsiei”, Diskret. matem., 36:1 (2024), 136–148
V. V. Lavrentev, “Slabaya skhodimost gilbertovoznachnykh semimartingalov k stokhasticheski nepreryvnomu protsessu s nezavisimymi prirascheniyami”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2024, no. 1, 5–16
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
V. V. Lavrentev, A. L. Bugrimov, “Usloviya kompaktnosti semeistva mer gilbertovoznachnykh nepreryvnykh semimartingalov”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2019, no. 4, 39–51
E. Mordecki, “Necessary Conditions for Stable Convergenceof Semimartingales”, Theory Probab Appl, 44:1 (2000), 217
A. F. Taraskin, “On the limiting behaviour of the likelihood ratio for semimartingales”, Russian Math. Surveys, 40:2 (1985), 237–238
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
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
Grigelionis B., Mikulevicius R., “On Contiguity and Weak-Convergence of Probability-Measures”, 1021, 1983, 177–194
B. I. Grigelionis, K. Kubilyus, R. A. Mikulyavichyus, “The martingale approach to functional limit theorems”, Russian Math. Surveys, 37:6 (1982), 41–54
Citation in format AMSBIB
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