scholarly journals Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions

1986 ◽  
Vol 104 (1) ◽  
pp. 1-19 ◽  
Author(s):  
C. Kipnis ◽  
S. R. S. Varadhan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Processes ◽  
Additive Functionals ◽  
Reversible Markov Processes

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.

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