A general central limit theorem for strong mixing sequences

2014 ◽  
Vol 94 ◽  
pp. 236-238 ◽  
Author(s):  
Magnus Ekström
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Strong Mixing ◽  
Mixing Sequences ◽  
Strong Mixing Sequences

A Central Limit Theorem with Conditioning on the Distant Past

1975 ◽  
Vol 18 (2) ◽  
pp. 245-247
Author(s):  
D. L. McLeish
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Strong Mixing ◽  
Mixing Sequences ◽  
Strong Mixing Sequences

Serfling (1968) has considered a central limit theorem in which assumptions are made concerning the expectation of variables conditioned on their distant predecessors. Dvoretsky (1972, theorem 5.3) has continued this investigation. Serfling showed that both martingales and φ-mixing sequences satisfied his conditions, and Dvoretsky extended this to Strong mixing sequences of random variables.

A Central Limit Theorem for an Array of Strong Mixing Random Fields

2000 ◽  
pp. 289-304
Author(s):  
Tucker McElroy ◽  
Dimitris N. Politis
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Strong Mixing ◽  
Mixing Random Fields

A Central Limit Theorem and Law of the Iterated Logarithm for a Random Field with Exponential Decay of Correlations

2004 ◽  
Vol 56 (1) ◽  
pp. 209-224 ◽  
Author(s):  
Byron Schmuland ◽  
Wei Sun
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Field ◽  
Central Limit ◽  
Exponential Decay ◽  
Gibbs Measures ◽  
Strong Mixing ◽  
Iterated Logarithm ◽  
Exponential Decay Of Correlations ◽  
The Law

AbstractIn [6], Walter Philipp wrote that “… the law of the iterated logarithm holds for any process for which the Borel-Cantelli Lemma, the central limit theorem with a reasonably good remainder and a certain maximal inequality are valid.” Many authors [1], [2], [4], [5], [9] have followed this plan in proving the law of the iterated logarithm for sequences (or fields) of dependent random variables.We carry on this tradition by proving the law of the iterated logarithm for a random field whose correlations satisfy an exponential decay condition like the one obtained by Spohn [8] for certain Gibbs measures. These do not fall into the ϕ-mixing or strong mixing cases established in the literature, but are needed for our investigations [7] into diffusions on configuration space.The proofs are all obtained by patching together standard results from [5], [9] while keeping a careful eye on the correlations.

Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach

1973 ◽  
Vol 5 (01) ◽  
pp. 119-137 ◽  
Author(s):  
D. J. Scott
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Functional Central Limit Theorem ◽  
Stationary Increments ◽  
Mixing Sequences ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit

The Skorokhod representation for martingales is used to obtain a functional central limit theorem (or invariance principle) for martingales. It is clear from the method of proof that this result may in fact be extended to the case of triangular arrays in which each row is a martingale sequence and the second main result is a functional central limit theorem for such arrays. These results are then used to obtain two functional central limit theorems for processes with stationary ergodic increments following on from the work of Gordin. The first of these theorems extends a result of Billingsley for Φ-mixing sequences.

scholarly journals Convergence of Weighted Linear Process forρ-Mixing Random Variables

2007 ◽  
Vol 2007 ◽  
pp. 1-7
Author(s):  
Guang-Hui Cai
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Linear Process ◽  
Functional Central Limit Theorem ◽  
Mixing Sequences ◽  
Functional Central Limit ◽  
Mixing Random Variables

A central limit theorem and a functional central limit theorem are obtained for weighted linear process ofρ-mixing sequences for theXt=∑i=0∞aiYt−i, where{Yi,0≤i<∞}is a sequence ofρ-mixing random variables withEYi=0,0<EYi2<∞,∑i=1∞ρ(2i)<∞. The results obtained generalize the results of Liang et al. (2004) toρ-mixing sequences.

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