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Teor. Veroyatnost. i Primenen., 1980, Volume 25, Issue 4, Pages 683–703 (Mi tvp1225)  

This article is cited in 11 scientific papers (total in 13 papers)

A functional central limit theorem for semimartingales

R. Š. Lipčer, A. N. Širyaev


Abstract: Let $X^n$, $n\geqslant 1$, be a sequence of semimartingales with triplets of local characteristics $T^n=(B^n,\langle X^{cn}\rangle,\nu^n)$ and let $X$ be a continuous Gaussian martingale with a triplet $T=(0,\langle X\rangle,0)$. We give conditions on the convergence of the triplets $T^n$ to $T$ which are sufficient for the weak convergence of the distributions of $X^n$ to the distribution of $X$ and for the weak convergence of the finite-dimensional distributions of $X^n$ to the corresponding finite-dimensional distributions of $X$.

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English version:
Theory of Probability and its Applications, 1981, 25:4, 667–688

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Received: 25.03.1980

Citation: R. Š. Lipčer, A. N. Širyaev, “A functional central limit theorem for semimartingales”, Teor. Veroyatnost. i Primenen., 25:4 (1980), 683–703; Theory Probab. Appl., 25:4 (1981), 667–688

Citation in format AMSBIB
\by R.~{\v S}.~Lip{\v{c}}er, A.~N.~{\v S}iryaev
\paper A functional central limit theorem for semimartingales
\jour Teor. Veroyatnost. i Primenen.
\yr 1980
\vol 25
\issue 4
\pages 683--703
\jour Theory Probab. Appl.
\yr 1981
\vol 25
\issue 4
\pages 667--688

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath
    2. V. V. Lavrent'ev, “The functional central limit theorem for semimartingales taking values in a Hilbert space”, Russian Math. Surveys, 37:4 (1982), 125–126  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. 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
    4. È. V. Khmaladze, “Some applications of the theory of martingales to statistics”, Russian Math. Surveys, 37:6 (1982), 215–237  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. M. Lozinskii, “On the hundredth anniversary of the birth of S. N. Bernstein”, Russian Math. Surveys, 38:3 (1983), 163–178  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. A. Butov, “On the problem of weak convergence of a sequence of semimartingales to a process of diffusion type”, Russian Math. Surveys, 38:5 (1983), 135–136  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. 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
    8. Kh. M. Mamatov, “Weak convergence of stochastic integrals with respect to semimartingales”, Russian Math. Surveys, 41:5 (1986), 155–156  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. R. M. Absava, “On the limit distribution of the quadratic deviation for a broad class of estimators of functional characteristics of the distribution law of observations”, Russian Math. Surveys, 56:5 (2001), 973–975  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. A. G. Sholomitskii, “On the necessary conditions of Poisson convergence for martingales”, Theory Probab. Appl., 49:4 (2005), 735–737  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. È. A. Nadaraya, G. A. Sokhadze, P. Babilua, “On some goodness-of-fit tests based on kernel density estimates”, Theory Probab. Appl., 54:2 (2010), 324–333  mathnet  crossref  crossref  mathscinet  isi
    12. È. A. Nadaraya, P. Babilua, G. A. Sokhadze, “On the integral square deviation of one nonparametric estimation of the Bernoulli regession”, Theory Probab. Appl., 57:2 (2013), 265–278  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. 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
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