Quenched Invariance Principles for Orthomartingale-Like Sequences

Magda Peligrad () and Dalibor Volný ()
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Magda Peligrad: University of Cincinnati
Dalibor Volný: LMRS, CNRS and Université de Rouen Normandie

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1238-1265

Abstract: Abstract In this paper, we study the central limit theorem and its functional form for random fields which are started not from their equilibrium, but rather under the measure conditioned by the past sigma field. The initial class considered is that of orthomartingales and then the result is extended to a more general class of random fields by approximating them, in some sense, with an orthomartingale. We construct an example which shows that there are orthomartingales which satisfy the CLT but not its quenched form. This example also clarifies the optimality of the moment conditions used for the validity of our results. Finally, by using the so-called orthomartingale-coboundary decomposition, we apply our results to linear and nonlinear random fields.

Keywords: Random fields; Quenched central limit theorem; Theorems started at a point; Orthomartingales; Coboundary; 60F05; 60G60; 60G42; 60G48 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-019-00914-z

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