Bounds for the Tail Distributions of Suprema of Sub-Gaussian Type Random Fields

被引：0

作者：

Hopkalo, Olha ^{[1
]}

Sakhno, Lyudmyla ^{[2
]}

Vasylyk, Olga ^{[3
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Fac Econ, Dept Econ Cybernet, Volodymyrska Str 64, UA-01601 Kiev, Ukraine

[2] Taras Shevchenko Natl Univ Kyiv, Fac Mech & Math, Dept Probabil Theory Stat & Actuarial Math, Volodymyrska Str 64, UA-01601 Kiev, Ukraine

[3] Natl Tech Univ Ukraine, Igor Sikorsky Kyiv Polytech Inst, Dept Math Anal & Probabil Theory, Perem Ave 37, UA-03056 Kiev, Ukraine

来源：

AUSTRIAN JOURNAL OF STATISTICS | 2023年 / 52卷

关键词：

sub-Gaussian random fields; distribution of supremum; heat equation; Airy equa-tion; random initial conditions; stochastic heat equation; HEAT-TYPE EQUATIONS;

D O I：

10.17713/ajs.v52iSI.1753

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The paper presents bounds for the distributions of suprema for particular classes of p-sub-Gaussian random fields. Results stated depend on representations of bounds for increments of the fields in different metrics. Several examples of applications are provided to illustrate the results, in particular, to random fields related to stochastic partial differential equations and partial differential equations with random initial conditions.

引用

页码：54 / 70

页数：17

共 50 条

[1] Bounds on tail probabilities for quadratic forms in dependent sub-gaussian random variables
Zajkowski, Krzysztof
STATISTICS & PROBABILITY LETTERS, 2020, 167
[2] Theory and generation of conditional, scalable sub-Gaussian random fields
Panzeri, M.
Riva, M.
Guadagnini, A.
Neuman, S. P.
WATER RESOURCES RESEARCH, 2016, 52 (03) : 1746 - 1761
[3] Some applications of the Malliavin calculus to sub-Gaussian and non-sub-Gaussian random fields
Vizcarra, Andrew B.
Viens, Frederi G.
SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS V, 2008, 59 : 363 - 395
[4] SUB-GAUSSIAN TAIL BOUNDS FOR THE WIDTH AND HEIGHT OF CONDITIONED GALTON-WATSON TREES
Addario-Berry, Louigi
Devroye, Luc
Janson, Svante
ANNALS OF PROBABILITY, 2013, 41 (02): : 1072 - 1087
[5] Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields
Bierme, Hermine
Lacaux, Celine
BERNOULLI, 2015, 21 (03) : 1719 - 1759
[6] Sub-Gaussian Error Bounds for Hypothesis Testing
Wang, Yan
2021 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2021, : 3050 - 3055
[7] INEQUALITIES FOR THE DISTRIBUTIONS OF FUNCTIONALS OF SUB-GAUSSIAN VECTORS
Buldygin, V. V.
Pechuk, E. D.
THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 2009, 80 : 23 - 33
[8] PARAMETER ESTIMATION OF SUB-GAUSSIAN STABLE DISTRIBUTIONS
Omelchenko, Vadym
KYBERNETIKA, 2014, 50 (06) : 929 - 949
[9] Simulation of a strictly sub-Gaussian random field
Turchyn, Ievgen
STATISTICS & PROBABILITY LETTERS, 2014, 92 : 183 - 189
[10] Unconditional Convergence of Sub-Gaussian Random Series
Giorgobiani, G.
Kvaratskhelia, V.
Menteshashvili, M.
PATTERN RECOGNITION AND IMAGE ANALYSIS, 2024, 34 (01) : 92 - 101

← 1 2 3 4 5 →