• Title/Summary/Keyword: ergodicity

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Ergodicity of Nonlinear Autoregression with Nonlinear ARCH Innovations

  • Hwang, S.Y.;Basawa, I.V.
    • Communications for Statistical Applications and Methods
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    • v.8 no.2
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    • pp.565-572
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    • 2001
  • This article explores the problem of ergodicity for the nonlinear autoregressive processes with ARCH structure in a very general setting. A sufficient condition for the geometric ergodicity of the model is developed along the lines of Feigin and Tweedie(1985), thereby extending classical results for specific nonlinear time series. The condition suggested is in turn applied to some specific nonlinear time series illustrating that our results extend those in the literature.

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Conditions for the Non-ergodicity of Some Markov Chains

  • Lee, Oesook
    • Journal of the Korean Statistical Society
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    • v.25 no.3
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    • pp.303-311
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    • 1996
  • We consider the discrete time randomly perturbed systems on sep-arable Banach space given by $X_{n+1};=;{Gamma}_{n+1}(X_n);+;{epsilon}_{n+1}$ where {${Gamma}_n$} is a sequence of random functions and {${epsilon}_n$} is a sequence of disturbances Sufficient conditions for non-ergodicity of {$X_n$} are obtained.

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Asymptotics of a class of markov processes generated by $X_{n+1}=f(X_n)+\epsilon_{n+1}$

  • Lee, Oe-Sook
    • Journal of the Korean Statistical Society
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    • v.23 no.1
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    • pp.1-12
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    • 1994
  • We consider the markov process ${X_n}$ on R which is genereated by $X_{n+1} = f(X_n) + \epsilon_{n+1}$. Sufficient conditions for irreducibility and geometric ergodicity are obtained for such Markov processes. In additions, when ${X_n}$ is geometrically ergodic, the functional central limit theorem is proved for every bounded functions on R.

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Uniform Ergodicity of an Exponential Continuous Time GARCH(p,q) Model

  • Lee, Oe-Sook
    • Communications for Statistical Applications and Methods
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    • v.19 no.5
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    • pp.639-646
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    • 2012
  • The exponential continuous time GARCH(p,q) model for financial assets suggested by Haug and Czado (2007) is considered, where the log volatility process is driven by a general L$\acute{e}$vy process and the price process is then obtained by using the same L$\acute{e}$vy process as driving noise. Uniform ergodicity and ${\beta}$-mixing property of the log volatility process is obtained by adopting an extended generator and drift condition.

Ergodic properties of compact actions on $C^{+}$-algebras

  • Jang, Sun-Young
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.289-295
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    • 1994
  • Let (A,G,.alpha.) be a $C^{*}$-dynamical system. In [3] the classical notions of ergodic properties of topological dynamical systems such as topological transitivity, minimality, and uniquely ergodicity are extended and analyzed in the context of non-abelian $C^{*}$-dynamical systems. We showed in [2] that if G is a compact group, then minimality, topological transitivity, uniquely ergodicity, and weakly ergodicity of the $C^{*}$-dynamical system (A,G,.alpha.) are equivalent.alent.

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A REMARK ON ERGODICITY OF QUANTUM MARKOVIAN SEMIGROUPS

  • Ko, Chul-Ki
    • Communications of the Korean Mathematical Society
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    • v.24 no.1
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    • pp.99-109
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    • 2009
  • The aim of this paper is to find the set of the fixed elements and the set of elements for which equality holds in Schwarz inequality for the KMS-symmetric Markovian semigroup $\{S_t\}_{t{\geq}0}$ given in [10]. As an application, we study some properties such as the ergodicity and the asymptotic behavior of the semigroup.

Uniform Ergodicity and Exponential α-Mixing for Continuous Time Stochastic Volatility Model

  • Lee, O.
    • Communications for Statistical Applications and Methods
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    • v.18 no.2
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    • pp.229-236
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    • 2011
  • A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general L$\'{e}$vy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential ${\alpha}$-mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.

On geometric ergodicity and ${\beta}$-mixing property of asymmetric power transformed threshold GARCH(1,1) process

  • Lee, Oe-Sook
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.2
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    • pp.353-360
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    • 2011
  • We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric ergodicity and ${\beta}$-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) is also considered as a special case.