On the History of the St. Petersburg School of Probability and Statistics. III. Distributions of Functionals of Processes, Stochastic Geometry, and Extrema

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On the History of the St. Petersburg School of Probability and Statistics. III. Distributions of Functionals of Processes, Stochastic Geometry, and Extrema. / Borodin, A. N.; Davydov, Yu A.; Nevzorov, V. B.

In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 4, 01.10.2018, p. 343-359.

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

BibTeX

@article{7c034716aa04412ba53c9c971171f1ab,

title = "On the History of the St. Petersburg School of Probability and Statistics. III. Distributions of Functionals of Processes, Stochastic Geometry, and Extrema",

abstract = "This is the third paper in a series of reviews devoted to the scientific achievements of the Leningrad–St. Petersburg School of Probability and Statistics in 1947–2017. The paper deals with the studies on functionals of random processes, some problems of stochastic geometry, and problems associated with ordered systems of random variables. The first sections of the paper are devoted to the problems of calculating the distributions of various functionals of Brownian motion and consider the so-called invariance principles for Brownian local times and random walks. The second part is dedicated to limit theorems for weakly dependent random variables and local limit theorems for stochastic functionals. It provides information about the stratification method and the local invariance principle. The asymptotic behavior of the convex hulls of random samples of increasing size and limit theorems for random zonotopes are also considered. An important relation between Poisson point processes and stable distributions is explained. The final part presents extensive information on research related to ordered systems of random variables. The maxima of sequential sums, order statistics, and record values are analyzed in detail.",

keywords = "Brownian local time, Brownian motion, distribution of functionals, extrema, invariance principle, limit theorems for random zonotopes and convex hulls, local invariance principle, order statistics, random walks, records, stratification method",

author = "Borodin, {A. N.} and Davydov, {Yu A.} and Nevzorov, {V. B.}",

year = "2018",

month = oct,

day = "1",

doi = "10.3103/S1063454118040052",

language = "English",

volume = "51",

pages = "343--359",

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

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - On the History of the St. Petersburg School of Probability and Statistics. III. Distributions of Functionals of Processes, Stochastic Geometry, and Extrema

AU - Borodin, A. N.

AU - Davydov, Yu A.

AU - Nevzorov, V. B.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - This is the third paper in a series of reviews devoted to the scientific achievements of the Leningrad–St. Petersburg School of Probability and Statistics in 1947–2017. The paper deals with the studies on functionals of random processes, some problems of stochastic geometry, and problems associated with ordered systems of random variables. The first sections of the paper are devoted to the problems of calculating the distributions of various functionals of Brownian motion and consider the so-called invariance principles for Brownian local times and random walks. The second part is dedicated to limit theorems for weakly dependent random variables and local limit theorems for stochastic functionals. It provides information about the stratification method and the local invariance principle. The asymptotic behavior of the convex hulls of random samples of increasing size and limit theorems for random zonotopes are also considered. An important relation between Poisson point processes and stable distributions is explained. The final part presents extensive information on research related to ordered systems of random variables. The maxima of sequential sums, order statistics, and record values are analyzed in detail.

AB - This is the third paper in a series of reviews devoted to the scientific achievements of the Leningrad–St. Petersburg School of Probability and Statistics in 1947–2017. The paper deals with the studies on functionals of random processes, some problems of stochastic geometry, and problems associated with ordered systems of random variables. The first sections of the paper are devoted to the problems of calculating the distributions of various functionals of Brownian motion and consider the so-called invariance principles for Brownian local times and random walks. The second part is dedicated to limit theorems for weakly dependent random variables and local limit theorems for stochastic functionals. It provides information about the stratification method and the local invariance principle. The asymptotic behavior of the convex hulls of random samples of increasing size and limit theorems for random zonotopes are also considered. An important relation between Poisson point processes and stable distributions is explained. The final part presents extensive information on research related to ordered systems of random variables. The maxima of sequential sums, order statistics, and record values are analyzed in detail.

KW - Brownian local time

KW - Brownian motion

KW - distribution of functionals

KW - extrema

KW - invariance principle

KW - limit theorems for random zonotopes and convex hulls

KW - local invariance principle

KW - order statistics

KW - random walks

KW - records

KW - stratification method

UR - http://www.scopus.com/inward/record.url?scp=85061215236&partnerID=8YFLogxK

U2 - 10.3103/S1063454118040052

DO - 10.3103/S1063454118040052

M3 - Article

AN - SCOPUS:85061215236

VL - 51

SP - 343

EP - 359

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 49897272