Invariance principle for martingale-difference random fields

DOI10.1016/S0167-7152(98)00020-0zbMath0910.60019MaRDI QIDQ1265969

Suren K. Poghosyan, Sylvie Roelly

Publication date: 6 April 1999

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

central limit theoreminvariance principlemartingale-difference random fieldmulti-parameter Wiener process

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Functional limit theorems; invariance principles (60F17)

Related Items (16)

Limit theorems for weighted Bernoulli random fields under Hannan's condition ⋮ Fractional Brownian sheet and martingale difference random fields ⋮ Semiparametric regression estimation for longitudinal data in models with martingale difference error's structure ⋮ Randomization in the construction of multidimensional martingales ⋮ Invariance principle via orthomartingale approximation ⋮ A local invariance principle for Gibbsian fields ⋮ Bound on the maximal function associated to the law of the iterated logarithms for Bernoulli random fields ⋮ ON FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LINEAR RANDOM FIELDS WITH DEPENDENT INNOVATIONS ⋮ Testing for epidemic changes in the mean of a multiparameter stochastic process ⋮ The invariance principle for linear multi-parameter stochastic processes generated by associated fields ⋮ High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus ⋮ Asymptotics for linear random fields ⋮ A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error's structure ⋮ A central limit theorem for fields of martingale differences ⋮ Estimating structural changes in regression quantiles ⋮ An invariance principle for stationary random fields under Hannan's condition

Cites Work

• Functional central limit theorem for martingale-difference random field
• Martingale-difference Gibbs random fields and central limit theorem
• Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications
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