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

Author

Listed:
  • Burdak, Zbigniew
  • Kosiek, Marek
  • Pagacz, Patryk
  • Słociński, Marek

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.

Suggested Citation

  • Burdak, Zbigniew & Kosiek, Marek & Pagacz, Patryk & Słociński, Marek, 2025. "An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process," Journal of Multivariate Analysis, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:jmvana:v:209:y:2025:i:c:s0047259x25000405
    DOI: 10.1016/j.jmva.2025.105445
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