scholarly journals Central Limit Theorems for the Local Times of Certain Markov Processes and the Squares of Gaussian Processes

1990 ◽  
Vol 18 (3) ◽  
pp. 1126-1140 ◽  
Author(s):  
Robert J. Adler ◽  
Michael B. Marcus ◽  
Joel Zinn
Keyword(s):  
Central Limit ◽  
Markov Processes ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Local Times

scholarly journals Central limit theorems for supercritical branching Markov processes

2014 ◽  
Vol 266 (3) ◽  
pp. 1716-1756 ◽  
Author(s):  
Yan-Xia Ren ◽  
Renming Song ◽  
Rui Zhang
Keyword(s):  
Central Limit ◽  
Markov Processes ◽  
Limit Theorems ◽  
Central Limit Theorems

Limit theorems for Markov processes via a variant of the Trotter-Kato theorem

1980 ◽  
Vol 17 (03) ◽  
pp. 704-715 ◽  
Author(s):  
Walter A. Rosenkrantz ◽  
C. C. Y. Dorea
Keyword(s):  
Central Limit ◽  
Markov Processes ◽  
Diffusion Approximation ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit

A variant of the Trotter–Kato theorem due to Kurtz (1969) is used to give new and simpler proofs of functional central limit theorems for Markov processes. Applications include theorems of Bellman and Harris (1951), Stone (1961), Karlin and McGregor (1965), Gihman and Skorokhod (1972) and Rosenkrantz (1975). In addition our methods yield a novel counterexample to the so-called ‘diffusion approximation'.

scholarly journals Nonparametric density estimators based on nonstationary absolutely regular random sequences

1996 ◽  
Vol 9 (3) ◽  
pp. 233-254 ◽  
Author(s):  
Michel Harel ◽  
Madan L. Puri
Keyword(s):  
Central Limit ◽  
Markov Processes ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Density Estimator ◽  
Random Sequences ◽  
Arma Processes ◽  
Density Estimators

In this paper, the central limit theorems for the density estimator and for the integrated square error are proved for the case when the underlying sequence of random variables is nonstationary. Applications to Markov processes and ARMA processes are provided.

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