scholarly journals Exact moderate and large deviations for linear random fields

2018 ◽  
Vol 55 (2) ◽  
pp. 431-449 ◽  
Author(s):  
Hailin Sang ◽  
Yimin Xiao
Keyword(s):  
Large Deviations ◽  
Random Field ◽  
Nonparametric Regression ◽  
Random Fields ◽  
Limit Theorems ◽  
Large Deviation ◽  
Strong Limit ◽  
Field Errors

Abstract By extending the methods of Peligrad et al. (2014), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with random field errors and strong limit theorems.

scholarly journals Cramér type moderate deviations for random fields

2019 ◽  
Vol 56 (01) ◽  
pp. 223-245 ◽  
Author(s):  
Aleksandr Beknazaryan ◽  
Hailin Sang ◽  
Yimin Xiao
Keyword(s):  
Random Field ◽  
Nonparametric Regression ◽  
Random Fields ◽  
Long Memory ◽  
Moderate Deviation ◽  
Moderate Deviations ◽  
Partial Sums ◽  
Field Errors

AbstractWe study the Cramér type moderate deviation for partial sums of random fields by applying the conjugate method. The results are applicable to the partial sums of linear random fields with short or long memory and to nonparametric regression with random field errors.

scholarly journals Orthomartingale-coboundary decomposition for stationary random fields

2016 ◽  
Vol 16 (05) ◽  
pp. 1650017 ◽  
Author(s):  
Mohamed El Machkouri ◽  
Davide Giraudo
Keyword(s):  
Large Deviations ◽  
Random Field ◽  
Random Fields ◽  
Decomposition Method ◽  
Limit Theorems ◽  
Stationary Random Fields

We provide a new projective condition for a stationary real random field indexed by the lattice [Formula: see text] to be well approximated by an orthomartingale in the sense of Cairoli (1969). Our main result can be viewed as a multidimensional version of the martingale-coboundary decomposition method which the idea goes back to Gordin (1969). It is a powerful tool for proving limit theorems or large deviations inequalities for stationary random fields when the corresponding result is valid for orthomartingales.

The multitype branching random walk: temporal and spatial limit theorems

1989 ◽  
Vol 21 (03) ◽  
pp. 491-512
Author(s):  
B. Gail Ivanoff
Keyword(s):  
Random Walk ◽  
Random Field ◽  
Random Fields ◽  
Limit Theorems ◽  
Branching Random Walk ◽  
Initial Field ◽  
Large Numbers ◽  
Poisson Random Fields ◽  
The Mean ◽  
Temporal And Spatial

We consider a multitype branching random walk with independent Poisson random fields of each type of particle initially. The existence of limiting random fields as the generation number, is studied, when the intensity of the initial field is renormalized in such a way that the mean measures converge. Spatial laws of large numbers and central limit theorems are given for the limiting random field, when it is non-trivial.

scholarly journals ON FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LINEAR RANDOM FIELDS WITH DEPENDENT INNOVATIONS

2008 ◽  
Vol 49 (4) ◽  
pp. 533-541 ◽  
Author(s):  
MI-HWA KO ◽  
HYUN-CHULL KIM ◽  
TAE-SUNG KIM
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Random Field ◽  
Central Limit ◽  
Random Fields ◽  
Limit Theorems ◽  
Sufficient Conditions ◽  
Standard Brownian Motion ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit

AbstractFor a linear random field (linear p-parameter stochastic process) generated by a dependent random field with zero mean and finite qth moments (q>2p), we give sufficient conditions that the linear random field converges weakly to a multiparameter standard Brownian motion if the corresponding dependent random field does so.

Large Deviations and Ratio Limit Theorems for Pattern-Avoiding Permutations

2013 ◽  
Vol 23 (2) ◽  
pp. 161-200 ◽  
Author(s):  
MAHSHID ATAPOUR ◽  
NEAL MADRAS
Keyword(s):  
Large Deviations ◽  
Limit Theorems ◽  
Large Deviation ◽  
Corner Points ◽  
Set Of Permutations ◽  
Ratio Limit Theorems ◽  
Ratio Limit ◽  
Left Corner ◽  
To Come ◽  
Pattern Avoiding Permutations

For a fixed permutation τ, let$\mathcal{S}_N(\tau)$be the set of permutations onNelements that avoid the pattern τ. Madras and Liu (2010) conjectured that$\lim_{N\rightarrow\infty}\frac{|\mathcal{S}_{N+1}(\tau)|}{ |\mathcal{S}_N(\tau)|}$exists; if it does, it must equal the Stanley–Wilf limit. We prove the conjecture for every permutation τ of length 5 or less, as well as for some longer cases (including 704 of the 720 permutations of length 6). We also consider permutations drawn at random from$\mathcal{S}_N(\tau)$, and we investigate properties of their graphs (viewing permutations as functions on {1,. . .,N}) scaled down to the unit square [0,1]2. We prove exact large deviation results for these graphs when τ has length 3; it follows, for example, that it is exponentially unlikely for a random 312-avoiding permutation to have points above the diagonal strip |y−x| < ε, but not unlikely to have points below the strip. For general τ, we show that some neighbourhood of the upper left corner of [0,1]2is exponentially unlikely to contain a point of the graph if and only if τ starts with its largest element. For patterns such as τ=4231 we establish that this neighbourhood can be extended along the sides of [0,1]2to come arbitrarily close to the corner points (0,0) and (1,1), as simulations had suggested.

The multitype branching random walk: temporal and spatial limit theorems

1989 ◽  
Vol 21 (3) ◽  
pp. 491-512 ◽  
Author(s):  
B. Gail Ivanoff
Keyword(s):  
Random Walk ◽  
Random Field ◽  
Random Fields ◽  
Limit Theorems ◽  
Branching Random Walk ◽  
Initial Field ◽  
Large Numbers ◽  
Poisson Random Fields ◽  
The Mean ◽  
Temporal And Spatial

We consider a multitype branching random walk with independent Poisson random fields of each type of particle initially. The existence of limiting random fields as the generation number, is studied, when the intensity of the initial field is renormalized in such a way that the mean measures converge. Spatial laws of large numbers and central limit theorems are given for the limiting random field, when it is non-trivial.

Poisson and extreme value limit theorems for Markov random fields

1987 ◽  
Vol 19 (01) ◽  
pp. 106-122 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Random Fields ◽  
Conditional Distribution ◽  
Markov Random Fields ◽  
Limit Theorems ◽  
Nearest Neighbor ◽  
Extreme Value ◽  
Markov Random ◽  
Corner Points

Let Xt , be a Markov random field assuming values in RM. Let In be a rectangular box in Zm with its center at 0 and corner points with coordinates ±n. Let (An ) be a sequence of measurable subsets of RM such that neighborhood of t) → 0, for n → ∞; and let fn (x) be the indicator of An. Under appropriate conditions on the nearest-neighbor distributions of (Xt ), the conditional distribution of given the values of Xs , for s on the boundary of In , converges to the Poisson distribution. An immediate application is an extreme value limit theorem for a real-valued Markov random field.

Poisson and extreme value limit theorems for Markov random fields

1987 ◽  
Vol 19 (1) ◽  
pp. 106-122 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Random Fields ◽  
Conditional Distribution ◽  
Markov Random Fields ◽  
Limit Theorems ◽  
Nearest Neighbor ◽  
Extreme Value ◽  
Markov Random ◽  
Corner Points

Let Xt, be a Markov random field assuming values in RM. Let In be a rectangular box in Zm with its center at 0 and corner points with coordinates ±n. Let (An) be a sequence of measurable subsets of RM such that neighborhood of t) → 0, for n → ∞; and let fn(x) be the indicator of An. Under appropriate conditions on the nearest-neighbor distributions of (Xt), the conditional distribution of given the values of Xs, for s on the boundary of In, converges to the Poisson distribution. An immediate application is an extreme value limit theorem for a real-valued Markov random field.

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