Subadditive Ergodic Theory

Kingmán, J. F. C.

doi:10.1214/aop/1176996798

Cited by 561 publications

(353 citation statements)

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“…Provided that E(ln + A(E 0 , 0) ) < ∞ which follows from condition A4, Kingman's subadditive ergodic theorem (Kingman 1973) implies that there exists γ such that…”

Section: Persistence and Extinctionmentioning

confidence: 99%

Persistence of structured populations in random environments

Benaı̈m

Schreiber

2009

Theoretical Population Biology

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“…Provided that E(ln + A(E 0 , 0) ) < ∞ which follows from condition A4, Kingman's subadditive ergodic theorem (Kingman 1973) implies that there exists γ such that…”

Section: Persistence and Extinctionmentioning

confidence: 99%

Persistence of structured populations in random environments

Benaı̈m

Schreiber

2009

Theoretical Population Biology

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“…If equality holds, the process is called additive. Then we have the subadditive ergodic theorem by Kingman [148] (see [214] for a simple proof).…”

Section: The Lyapunov Exponent and The Density Of Statesmentioning

confidence: 99%

Jacobi Operators and Completely Integrable Nonlinear Lattices

Teschl

1999

Mathematical Surveys and Monographs

323

349

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Abstract. This book is intended to serve both as an introduction and a reference to spectral and inverse spectral theory of Jacobi operators (i.e., second order symmetric difference operators) and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.Starting from second order difference equations we move on to self-adjoint operators and develop discrete Weyl-Titchmarsh-Kodaira theory, covering all classical aspects like Weyl m-functions, spectral functions, the moment problem, inverse spectral theory, and uniqueness results. Next, we investigate some more advanced topics like locating the essential, absolutely continuous, and discrete spectrum, subordinacy, oscillation theory, trace formulas, random operators, almost periodic operators, (quasi-)periodic operators, scattering theory, and spectral deformations.Then, the Lax approach is used to introduce the Toda hierarchy and its modified counterpart, the Kac-van Moerbeke hierarchy. Uniqueness and existence theorems for the initial value problem, solutions in terms of Riemann theta functions, the inverse scattering transform, Bäcklund transformations, and soliton solutions are discussed.Corrections and complements to this book are available from:

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“…The preceding result of Cohen follows from the general subadditive ergodic theory of Kingman (1973). The determination of ξ is, however, a generally hard problem, except that for the scaler case, i.e.…”

Section: θ))mentioning

confidence: 85%

A note on the invertibility of nonlinear ARMA models

Chan¹,

Tong²

2010

Journal of Statistical Planning and Inference

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We review the concepts of local and global invertibility for a nonlinear auto-regressive moving-average (NLARMA) model. Under very general conditions, a local invertibility analysis of a NLARMA model admits the generic dichotomy that the innovation reconstruction errors either diminish geometrically fast or grow geometrically fast. We derive a simple sufficient condition for a NLARMA model to be locally invertible. The invertibility of the polynomial MA models is revisited. Moreover, we show that the Threshold MA models may be globally invertible even though some component MA models are non-invertible. One novelty of our approach is its cross-fertilization with dynamical systems.

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Subadditive Ergodic Theory

Cited by 561 publications

References 0 publications

Persistence of structured populations in random environments

Persistence of structured populations in random environments

Jacobi Operators and Completely Integrable Nonlinear Lattices

A note on the invertibility of nonlinear ARMA models

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