On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables

Standard

On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables. / Лифшиц, Михаил Анатольевич ; Ибрагимов, Ильдар Абдуллович ; Назаров, Александр Ильич; Запорожец, Дмитрий.

In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 3, 01.07.2018, p. 213-236.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{5086c4f08ec24877a9502a054698e713,

title = "On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables",

abstract = "This is the second paper in a series of reviews devoted to the scientific achievements of the Leningrad and St. Petersburg school of probability and mathematical statistics from 1947 to 2017. This paper is devoted to the works on limit theorems for dependent variables (in particular, Markov chains, sequences with mixing properties, and sequences admitting a martingale approximation) and to various aspects of the theory of random processes. We pay particular attention to Gaussian processes, including isoperimetric inequalities, estimates of the probabilities of small deviations in various norms, and the functional law of the iterated logarithm. We present a brief review and bibliography of the works on approximation of random fields with a parameter of growing dimension and probabilistic models of systems of sticky inelastic particles (including laws of large numbers and estimates for the probabilities of large deviations).",

keywords = "теория вероятностей, математическая статистика, approximation of processes of growing dimension, functional law of iterated logarithm, Gaussian processes, limit theorem for sums of dependent variables, small deviation probabilities, sticky particle systems",

author = "Лифшиц, {Михаил Анатольевич} and Ибрагимов, {Ильдар Абдуллович} and Назаров, {Александр Ильич} and Дмитрий Запорожец",

year = "2018",

month = jul,

day = "1",

doi = "10.3103/S1063454118030123",

language = "English",

volume = "51",

pages = "213--236",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables

AU - Лифшиц, Михаил Анатольевич

AU - Ибрагимов, Ильдар Абдуллович

AU - Назаров, Александр Ильич

AU - Запорожец, Дмитрий

PY - 2018/7/1

Y1 - 2018/7/1

N2 - This is the second paper in a series of reviews devoted to the scientific achievements of the Leningrad and St. Petersburg school of probability and mathematical statistics from 1947 to 2017. This paper is devoted to the works on limit theorems for dependent variables (in particular, Markov chains, sequences with mixing properties, and sequences admitting a martingale approximation) and to various aspects of the theory of random processes. We pay particular attention to Gaussian processes, including isoperimetric inequalities, estimates of the probabilities of small deviations in various norms, and the functional law of the iterated logarithm. We present a brief review and bibliography of the works on approximation of random fields with a parameter of growing dimension and probabilistic models of systems of sticky inelastic particles (including laws of large numbers and estimates for the probabilities of large deviations).

AB - This is the second paper in a series of reviews devoted to the scientific achievements of the Leningrad and St. Petersburg school of probability and mathematical statistics from 1947 to 2017. This paper is devoted to the works on limit theorems for dependent variables (in particular, Markov chains, sequences with mixing properties, and sequences admitting a martingale approximation) and to various aspects of the theory of random processes. We pay particular attention to Gaussian processes, including isoperimetric inequalities, estimates of the probabilities of small deviations in various norms, and the functional law of the iterated logarithm. We present a brief review and bibliography of the works on approximation of random fields with a parameter of growing dimension and probabilistic models of systems of sticky inelastic particles (including laws of large numbers and estimates for the probabilities of large deviations).

KW - теория вероятностей

KW - математическая статистика

KW - approximation of processes of growing dimension

KW - functional law of iterated logarithm

KW - Gaussian processes

KW - limit theorem for sums of dependent variables

KW - small deviation probabilities

KW - sticky particle systems

UR - http://www.scopus.com/inward/record.url?scp=85052813115&partnerID=8YFLogxK

U2 - 10.3103/S1063454118030123

DO - 10.3103/S1063454118030123

M3 - Article

VL - 51

SP - 213

EP - 236

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 35792842