Central limit theorem and invariance principle for associated random fields

2021 ◽  
Author(s):  
Abdurakhman Mukhamedov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Fields

Central limit theorem for weakly dependent random fields with values in $l_p$ ($1 \lep \le2$) and $c_0$ spaces

2020 ◽  
Vol 2020 (1) ◽  
pp. 116-122
Author(s):  
D.S. Ruzieva ◽  
O.Sh. Sharipov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Weakly Dependent

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

Thermodynamic limit and central limit theorem for point random fields in non-ergodic case

1988 ◽  
Vol 26 (1) ◽  
pp. 1-15
Author(s):  
Krystyna Parczyk ◽  
Tomasz Masłowski
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Thermodynamic Limit ◽  
Random Fields

A central limit theorem for stationary random fields

1998 ◽  
Vol 110 (3) ◽  
pp. 397-426 ◽  
Author(s):  
J�r�me Dedecker
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Stationary Random Fields

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

scholarly journals Central limit theorem for a class of random measures associated with germ-grain models

1996 ◽  
Vol 28 (02) ◽  
pp. 333-334
Author(s):  
Lothar Heinrich ◽  
Ilya S. Molchanov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Boolean Model ◽  
Random Sets ◽  
Model Parameters ◽  
Random Measures ◽  
Intrinsic Volumes ◽  
Individual Grains

We introduce a family of stationary random measures in the Euclidean space generated by so-called germ-grain models. The germ-grain model is defined as the union of i.i.d. compact random sets (grains) shifted by points (germs) of a point process. This model gives rise to random measures defined by the sum of contributions of non-overlapping parts of the individual grains. The corresponding moment measures are calculated and an ergodic theorem is presented. The main result is the central limit theorem for the introduced random measures, which is valid for rather general independently marked germ-grain models, including those with non-Poisson distribution of germs and non-convex grains. The technique is based on a central limit theorem for β-mixing random fields. It is shown that this construction of random measures includes those random measures obtained by the so-called positive extensions of intrinsic volumes. In the Poisson case it is possible to prove a central limit theorem under weaker assumptions by using approximations by m-dependent random fields. Applications to statistics of the Boolean model are also discussed. They include a standard way to derive limit theorems for estimators of the model parameters.

A central limit theorem for super-Brownian motion with super-Brownian immigration

1999 ◽  
Vol 36 (4) ◽  
pp. 1218-1224 ◽  
Author(s):  
Wen-Ming Hong ◽  
Zeng-Hu Li
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Potential Operator ◽  
Super Brownian Motion

We prove a central limit theorem for the super-Brownian motion with immigration governed by another super-Brownian. The limit theorem leads to Gaussian random fields in dimensions d ≥ 3. For d = 3 the field is spatially uniform; for d ≥ 5 its covariance is given by the potential operator of the underlying Brownian motion; and for d = 4 it involves a mixture of the two kinds of fluctuations.

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