A central limit theorem for a sequence of conditionally centered and α-mixing random fields

01/21/2023

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by   Abdollah Jalilian, et al.

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A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain α-mixing conditions in space or/and time. The limiting normal distribution is obtained for increasing spatial domain, increasing length of the sequence or a combination of these. The applicability of the theorem is demonstrated by examples regarding estimating functions for a space-time point process and a space-time Markov process.