WEAK CONVERGENCE TO LEVY STABLE PROCESSES IN DYNAMICAL SYSTEMS

被引：24

作者：

Tyran-Kaminska, Marta ^{[1
]}

机构：

[1] Univ Silesia, Inst Math, PL-40007 Katowice, Poland

来源：

STOCHASTICS AND DYNAMICS | 2010年 / 10卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Levy stable processes; functional limit theorem; Skorohod topology; piecewise monotonic maps; hitting times; Poisson distribution; LIMIT-THEOREMS; INVARIANCE-PRINCIPLE; MIXING SEQUENCES; MAPS; STATISTICS; FRACTIONS; INTERVAL; POINTS; DECAY; LAW;

D O I：

10.1142/S0219493710002942

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：

We study convergence of normalized ergodic sum processes to Levy stable process in the Skorohod space with J(1)-topology. Our necessary and sufficient conditions allow us to prove or disprove such convergence for specific examples.

引用

页码：263 / 289

页数：27

共 50 条

[1] Weak convergence to stable Levy processes for nonuniformly hyperbolic dynamical systems
Melbourne, Ian
Zweimueller, Roland
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2015, 51 (02): : 545 - 556
[2] Convergence to Levy stable processes under some weak dependence conditions
Tyran-Kaminska, Marta
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2010, 120 (09) : 1629 - 1650
[3] On weak convergence of sampled dynamical systems
Guillotin-Plantard, N
ANNALES DE L INSTITUT FOURIER, 2004, 54 (01) : 211 - +
[4] On weak convergence of sampled dynamical systems
Guillotin-Plantard, N
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (06): : 583 - 588
[5] ALMOST SURE WEAK-CONVERGENCE OF THE INCREMENTS OF LEVY PROCESSES
WSCHEBOR, M
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1995, 55 (02) : 253 - 270
[6] Weak convergence of censored and reflected stable processes
Kim, Panki
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2006, 116 (12) : 1792 - 1814
[7] Weak averaging principle for multiscale stochastic dynamical systems driven by stable processes
Zhang, Yanjie
Huang, Qiao
Wang, Xiao
Wang, Zibo
Duan, Jinqiao
JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 379 : 721 - 761
[8] Weak convergence of dynamical systems in two timescales
Basak, Gopal K.
Dasgupta, Amites
SYSTEMS & CONTROL LETTERS, 2020, 142
[9] Weak convergence of dynamical systems in two timescales
Basak, Gopal K.
Dasgupta, Amites
Systems and Control Letters, 2020, 142
[10] Superposition of chaotic processes with convergence to Levy's stable law
Umeno, K
PHYSICAL REVIEW E, 1998, 58 (02): : 2644 - 2647

← 1 2 3 4 5 →