Limit theorems for iterated random functions

By Wei Biao Wu, Xiaofeng Shao. Journal of Applied Probability, 2004

212 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6f281e6408b0cfa9a6b33d4ab097df608c1b38e3

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Citations in the corpus

Asymptotic theory for stationary processes (2011, background): “…distributions of iterated random functions and the related convergence issues has been extensively studied (Barnsley and Elton (1988), Elton (1990), Duflo (1997), Arnold (1998), Diaconis and Freedman (1999), Steinsaltz (1999), Alsmeyer and Fuh (2001), Jarner and Tweedie (2001), Wu and Shao (2004)).”
Count Time Series: A Methodological Review (2021, methodology): “In the latter, the theory of iterated random functions is used as developed in Diaconis and Freedman (1999) and Wu and Shao (2004).”
Theory and inference for a class of nonlinear models with application to time series of counts (2016, methodology): “The construction of the two chains agrees with the definition of geometric moment contraction (Definition 1 in Wu and Shao (2004)), so it follows from Proposition 1 that E|X ′ n −X ′′ n| ≤ (a+ b)n for all n.”
TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS (2010, methodology): “By Proposition 2 in Wu and Shao (2004), |cum(u−k1 ,u−k2 ,u−k3 ,u−k4)| ≤ Crmax(k1,k2,k3,k4)−min(k1,k2,k3,k4) for some r ∈ (0,1).”
Probability and moment inequalities under dependence (2013, background): “(2.18) By Theorem 2 in Wu and Shao (2004), conditions (2.17) and (2.18) imply that (2.16) has a stationary ergodic solution with ∥X0∥p ≤ |x0|+ κp/(1− Lp) =: Kp.”
A bootstrap-assisted spectral test of white noise under unknown dependence (2011, background): “If Xt admits the form (4), then (10) is true provided that Xt satisfies GMC(8) (see Wu and Shao, 2004, Proposition 2).”
Split invariance principles for stationary processes. (2011, unknown): “Results from Shao and Wu [44] show that under some simple technical assumption on G ∥∥Yk − Y (m) k ∥∥p exp(−ρm) holds with some p > 0 and ρ > 0.”
A survey of average contractive iterated function systems (2012, background): “Wu and Woodroofe [50], Alsmeyer and Fuh [1], Jarner and Tweedie [28], Iosifescu [23], Wu and Shao [49] and Herkenrath and Iosifescu [20].”
Covariance and precision matrix estimation for high-dimensional time series (2013, background): “…two conditions: (i) there exists some x 0 such that g ( x 0 , e 0 ) 2 q < ∞ and (ii) Then, it can be shown that z i deﬁned in (29) has a stationary ergodic distribution z 0 ∈ L 2 q and, in addition, ( z i ) has the geometric moment contraction (GMC) property; see Wu and Shao (2004) for details.”
Asymptotic spectral theory for nonlinear time series (2006, background): “Moreover, the GMC condition provides a convenient framework for a limit theory for nonlinear time series; see [32, 75] and [76].”
Quantile Spectral Processes: Asymptotic Analysis and Inference (2014, unknown): “Proofs and additional examples can be found in Shao and Wu [50] and Shao [49].”
M-estimation of linear models with dependent errors (2004, background): “Proposition 6 follows from Theorem 2 in [65].”
STRONG INVARIANCE PRINCIPLES FOR DEPENDENT RANDOM VARIABLES (2007, background): “LIL for stationary processes has been studied by Philipp [42], Reznik [47], Hall and Heyde [23], Stout [55], Rio [48], Volný and Samek [61] and Zhao and Woodroofe [72] among others.”
Self-Excited Threshold Poisson Autoregression (2013, background): “Davis and Liu (2012) generalized the conditional distribution of {Yt } to a one-parameter exponential family and took advantage of the theory for iterated random functions (Diaconis and Freedman 1999; Wu and Shao 2004) to establish stationarity and absolute regularity of the process, as well as the ”