scholarly journals Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

2012 ◽  
Vol 122 (5) ◽  
pp. 2155-2184 ◽  
Author(s):  
Tomasz Komorowski ◽  
Anna Walczuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Processes ◽  
Spectral Gap ◽  
Wasserstein Metric

A central limit theorem for random coefficient autoregressive models and ARCH/GARCH models

1998 ◽  
Vol 30 (1) ◽  
pp. 113-121 ◽  
Author(s):  
Andreas Rudolph
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Processes ◽  
Law Of Large Numbers ◽  
Random Systems ◽  
Autoregressive Models ◽  
Garch Models ◽  
Conditional Heteroscedasticity ◽  
Large Numbers

In this paper we study the so-called random coeffiecient autoregressive models (RCA models) and (generalized) autoregressive models with conditional heteroscedasticity (ARCH/GARCH models). Both models can be represented as random systems with complete connections. Within this framework we are led (under certain conditions) to CL-regular Markov processes and we will give conditions under which (i) asymptotic stationarity, (ii) a law of large numbers and (iii) a central limit theorem can be shown for the corresponding models.

scholarly journals On a Class of Markov Processes Taking Values on Lines and the Central Limit Theorem

1967 ◽  
Vol 30 ◽  
pp. 47-56 ◽  
Author(s):  
Masatoshi Fukushima ◽  
Masuyuki Hitsuda
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
State Space ◽  
Central Limit ◽  
Markov Processes ◽  
Continuous Time ◽  
Transition Function ◽  
Time Parameter ◽  
The Central Limit Theorem

We shall consider a class of Markov processes (n(t), x(t)) with the continuous time parameter t∈e[0, ∞), whose state space is {1, 2,..., N}×R1. We shall assume that the processes are spacially homogeneous with respect to X∈R1. In detail, our assumption is that the transition functionFij(x,t) = P(n(t) = j, x(t)≦x|n(0) = i,x(0) = 0), t > 0, 1≦i, j,≦N, x∈R1satisfies following conditions (1, 1)~(1,4).

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