Extreme value theory for non-uniformly expanding dynamical systems

Holland, Martin; Nicol, Matthew; Török, Andrei

doi:10.1090/s0002-9947-2011-05271-2

Cited by 54 publications

(103 citation statements)

References 30 publications

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“…On the other hand, EVLs for the partial maximum of dynamically defined stochas- tic processes is a much recent topic and have been proved directly in the recent papers [72,134,74,137,138,139,49,141,140,142,207,144,143]. We highlight the pioneering work of Collet [72] for the innovative ideas introduced.…”

Section: Non-exponential Lawsmentioning

confidence: 90%

“…It first appeared in the pioneering paper of Collet, [72], which has been an inspiration for plenty of the research on this issue. Then the subject has been further addressed and developed in many subsequent contributions including [134,73,135,74,136,137,138,139,49,140,81,46,76,77,78,141,142,79,44].…”

Section: Emergence Of Extreme Value Laws For Dynamical Systemsmentioning

confidence: 99%

“…Therefore, a substantial revision of the existing theory for stationary processes is needed in order to be able to prove the existence of EVL considering milder conditions on the dependence structure of the processes. This has been achieved first in the absence of clustering in [72,134,73,139]. The presence of clustering brings some extra difficulty in pursuing the weakening of condition D(u n ) of Leadbetter, eventually solved in [49].…”

Section: Extremes For General Stationary Processes -An Upgrade Motivamentioning

confidence: 99%

“…As an example, we do not discuss Lorenz-like interval maps considered in [139], where, moreover, these results have been extended to the relevant Lorenz flow.…”

Section: Interval Maps With Critical Pointsmentioning

confidence: 99%

“…This approach was first adopted in [72], and then applied more recently in [163,138,144,139,208,137]. We begin this chapter by reviewing this blocking argument approach.…”

Section: Introduction and Background On Extremes In Dynamical Systemsmentioning

confidence: 99%

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ii 4.1.2 The New Conditions 44 4.1.3 The Existence of EVL for General Stationary Stochastic Processes under Weaker Hypotheses 46 4.1.4 Proofs of Theorem 4.1.4 and Corollary 4.1.5 48 4.2 Extreme Values for Dynamically Defined Stochastic Processes 53 4.2.1 Observables and Corresponding Extreme Value Laws 55 4.2.2 Extreme Value Laws for Uniformly Expanding Systems 59 4.2.3 Example 4.2.1 revisited 61 4.2.4 Proof of the Dichotomy for Uniformly Expanding Maps 63 4.3 Point Processes of Rare Events 64 4.3.1 Absence of Clustering 64 4.3.2 Presence of Clustering 65 4.3.3 Dichotomy for Uniformly Expanding Systems for Point Processes 67 4.4 Conditions Д q (u n ), D 3 (u n ), D p (u n ) * and Decay of Correlations 68 4.5 Specific Dynamical Systems where the Dichotomy Applies 71 4.5.1 Rychlik Systems 72 4.5.2 Piecewise Expanding Maps in Higher Dimensions 73 4.6 Extreme Value Laws for Physical Observables 74

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Section: Non-exponential Lawsmentioning

confidence: 90%

Section: Emergence Of Extreme Value Laws For Dynamical Systemsmentioning

confidence: 99%

Section: Extremes For General Stationary Processes -An Upgrade Motivamentioning

confidence: 99%

“…As an example, we do not discuss Lorenz-like interval maps considered in [139], where, moreover, these results have been extended to the relevant Lorenz flow.…”

Section: Interval Maps With Critical Pointsmentioning

confidence: 99%

“…This approach was first adopted in [72], and then applied more recently in [163,138,144,139,208,137]. We begin this chapter by reviewing this blocking argument approach.…”

Section: Introduction and Background On Extremes In Dynamical Systemsmentioning

confidence: 99%

See 3 more Smart Citations