An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process

Zbigniew Burdak, Marek Kosiek, Patryk Pagacz and Marek Słociński

Journal of Multivariate Analysis, 2025, vol. 209, issue C

Abstract: A new approach to the evanescent part of a two-dimensional weak-stationary stochastic process with the past given by a half-plane is proceeded. The classical result due to Helson and Lowdenslager divides a two-parametric weak-stationary stochastic process into three parts. In this paper, we describe the most untouchable one — the evanescent part. Moreover, we point out how this part depends on the shape of the past.

Keywords: Evanescent part; Stochastic process; Weak-stationary; Isometies; Compatible isometries (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.jmva.2025.105445

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