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Teor. Veroyatnost. i Primenen., 1980, Volume 25, Issue 3, Pages 502–512 (Mi tvp1090)  

This article is cited in 2 scientific papers (total in 2 papers)

A new variant of the functional law of the iterated logarithm

A. V. Bulinskiĭ

Moscow

Abstract: The full description of the set of limit points of the sequence (3) is given, where $W(t)$ is a $d$-dimensional Brownian motion consisting of $d$ independent Brownian motions and $\varphi( \cdot )$ is arbitrary function such that $\varphi(t)\uparrow\infty$ ($t\uparrow\infty$). We show that with probability one this set coincides with the set $K_{R(\varphi)}$ specified in theorems 1–3. The sequences of the form (18) are also considered. The result of V. Strassen is a special case when $\varphi(t)=\sqrt{2\ln\ln t}$. The generalization of Hartman–Wintner's theorem is obtained. Theorems 4, 5 are valid for all sequences satisfying the almost sure invariance principles (martingale-differences, sequences with mixing etc.).

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English version:
Theory of Probability and its Applications, 1981, 25:3, 493–503

Bibliographic databases:

Received: 28.03.1979

Citation: A. V. Bulinskiǐ, “A new variant of the functional law of the iterated logarithm”, Teor. Veroyatnost. i Primenen., 25:3 (1980), 502–512; Theory Probab. Appl., 25:3 (1981), 493–503

Citation in format AMSBIB
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\jour Teor. Veroyatnost. i Primenen.
\yr 1980
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\issue 3
\pages 502--512
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\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 25
\issue 3
\pages 493--503
\crossref{https://doi.org/10.1137/1125061}
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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. A. V. Bulinski, M. A. Lifshits, “Rate of convergence in the functional law of the iterated logarithm with non-standard normalizing factors”, Russian Math. Surveys, 50:5 (1995), 925–944  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. P. Shashkin, “Generalization of the Law of the Iterated Logarithm for Associated Random Fields”, Math. Notes, 98:5 (2015), 831–842  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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