scholarly journals Central limit theorem for triangular arrays of non-homogeneous Markov chains

2011 ◽  
Vol 154 (3-4) ◽  
pp. 409-428 ◽  
Author(s):  
Magda Peligrad
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Markov Chains ◽  
Central Limit ◽  
Triangular Arrays

scholarly journals A martingale central limit theorem without negligibility conditions

1978 ◽  
Vol 18 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Sufficient Conditions ◽  
Infinitely Divisible ◽  
Martingale Central Limit Theorem ◽  
Triangular Arrays ◽  
Infinitely Divisible Laws ◽  
Martingale Case

We obtain sufficient conditions for the convergence of martingale triangular arrays to infinitely divisible laws with finite variances, without making the usual assumptions of uniform asymptotic negligibility. Our results generalise known results for both the martingale case under a negligibility assumption and the classical (independence) case without such assumptions.

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