Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps

Mariusz Mirek

Type: Article

Publication Date: 2010-07-20

Citations: 55

DOI: https://doi.org/10.1007/s00440-010-0312-9

View Publication

Download PDF

Locations

Probability Theory and Related Fields - View - PDF

Similar Works

Action	Title	Year	Authors
+	Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps	2009	Mariusz Mirek
+	Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps	2009	Mariusz Mirek
+	Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems	2010	Dariusz Buraczewski Ewa Damek Mariusz Mirek
+	Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems	2010	Dariusz Buraczewski Ewa Damek Mariusz Mirek
+	Iterated random functions and slowly varying tails	2015	Piotr Dyszewski
+	Iterated random functions and regularly varying tails	2017	Ewa Damek Piotr Dyszewski
+	Iterated random functions and regularly varying tails	2017	Ewa Damek Piotr Dyszewski
+	Iterated Random Functions and Slowly Varying Tails	2014	Piotr Dyszewski
+	Iterated Random Functions and Slowly Varying Tails	2014	Piotr Dyszewski
+ PDF Chat	Iterated random functions and regularly varying tails	2018	Ewa Damek Piotr Dyszewski
+ PDF Chat	Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems	2011	Dariusz Buraczewski Ewa Damek Mariusz Mirek
+	Empirical processes of iterated maps that contract on average	2012	Olivier Durieu
+	Empirical processes of iterated maps that contract on average	2012	Olivier Durieu
+	Iterated random maps and some classes of Markov processes	2001	Rabi Bhattacharya Edward C. Waymire
+	An Iterated Random Function with Lipschitz Number One	2003	Aaron Abrams H. G. Landau Zeph Landau James Pommersheim Eric Zaslow
+	An Iterated Random Function with Lipschitz Number One	2003	A. Abrams H. Landau Ziv Landau J. Pommersheim E. Zaslow
+	A simple proof of heavy tail estimates for affine type Lipschitz recursions	2016	Dariusz Buraczewski Ewa Damek
+	A simple proof of heavy tail estimates for affine type Lipschitz recursions	2016	Dariusz Buraczewski Ewa Damek
+	Iteration of IID Random Maps on R	2003	Krishna B. Athreya
+	On the stationary tail index of iterated random Lipschitz functions	2015	Gerold Alsmeyer

Works That Cite This (42)

Action	Title	Year	Authors
+	Tail estimates for stochastic fixed point equations via nonlinear renewal theory	2013	Jeffrey F. Collamore Anand N. Vidyashankar
+ PDF Chat	On the Recurrence Set of Planar Markov Random Walks	2012	Loı̈c Hervé Françoise Pène
+	On the stationary tail index of iterated random Lipschitz functions	2015	Gerold Alsmeyer
+	A simple proof of heavy tail estimates for affine type Lipschitz recursions	2016	Dariusz Buraczewski Ewa Damek
+	Markov tail chains	2013	Anja Janßen Johan Segers
+ PDF Chat	Importance sampling of heavy-tailed iterated random functions	2018	Bohan Chen Chang-Han Rhee Bert Zwart
+	Stable laws and spectral gap properties for affine random walks	2011	Zhiqiang Gao Yves Guivarc’h Émile Le Page
+ PDF Chat	Stable laws and spectral gap properties for affine random walks	2015	Zhiqiang Gao Yves Guivarc’h Émile Le Page
+	Stochastic recursions: Between Kesten’s and Grincevičius–Grey’s assumptions	2019	Ewa Damek Bartosz Kołodziejek
+	Iterated random functions and slowly varying tails	2015	Piotr Dyszewski

Works Cited by This (29)

Action	Title	Year	Authors
+	The Nagaev method via the Keller-Liverani theorem	2009	Loı̈c Hervé Françoise Pène
+ PDF Chat	The Nagaev-Guivarc’h method via the Keller-Liverani theorem	2010	Loı̈c Hervé Françoise Pène
+	A Central Limit Theorem for Contractive Stochastic Dynamical Systems	1998	Martin Benda
+ PDF Chat	Renewal Theory for Functionals of a Markov Chain with General State Space	1974	Harry Kesten
+ PDF Chat	Convergence to stable laws for a class of multidimensional stochastic recursions	2009	Dariusz Buraczewski Ewa Damek Yves Guivarc’h
+	On spectral properties of a family of transfer operators and convergence to stable laws for affine random walks	2008	Yves Guivarc’h Émile Le Page
+ PDF Chat	Implicit Renewal Theory and Tails of Solutions of Random Equations	1991	Charles M. Goldie
+ PDF Chat	Tail-homogeneity of stationary measures for some multidimensional stochastic recursions	2008	Dariusz Buraczewski Ewa Damek Yves Guivarc’h Andrzej Hulanicki Roman Urban
+ PDF Chat	Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps	2010	Sébastien Gouëzel
+ PDF Chat	Iterated random functions	2017	Persi Diaconis David A. Freedman