Limit theorems for iterated random functions by regenerative methods.

DOI10.1016/S0304-4149(01)00104-1zbMath1058.60054WikidataQ127213111 ScholiaQ127213111MaRDI QIDQ1766012

Gerold Alsmeyer, Cheng-Der Fuh

Publication date: 25 February 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

stationary distributionLipschitz mapProkhorov metricbackward iterationsiterated random functionforward iterationslevel \(\gamma \) ladder epochs

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Discrete-time Markov processes on general state spaces (60J05) Sample path properties (60G17) Renewal theory (60K05)

Related Items (10)

A survey of average contractive iterated function systems ⋮ Limit theorems for iterated random functions ⋮ WEAK DEPENDENCE: MODELS AND APPLICATIONS TO ECONOMETRICS ⋮ Multilevel linear models, Gibbs samplers and multigrid decompositions (with discussion) ⋮ On the stationary tail index of iterated random Lipschitz functions ⋮ Sieving random iterative function systems ⋮ Tail estimates for stochastic fixed point equations via nonlinear renewal theory ⋮ Consistency of Markov chain quasi-Monte Carlo on continuous state spaces ⋮ Stability of nonlinear stochastic recursions with application to nonlinear AR-GARCH models ⋮ Asymptotic behavior for Markovian iterated function systems

Cites Work

• Unnamed Item
• A multiplicative ergodic theorem for Lipschitz maps
• Ergodic theorems for iterated function systems controlled by regenerative sequences
• The random difference equation \(X_ n = A_ n X_{n-1} + B_ n\) in the critical case
• Some One-Sided Theorems on the Tail Distribution of Sample Sums with Applications to the Last Time and Largest Excess of Boundary Crossings
• Iterated Random Functions

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