Generalized stationary random fields with linear regressions - an operator approach

Wojciech Matysiak; Paweł J. Szabłowski

Generalized stationary random fields with linear regressions - an operator approach

Probability 2011-09-15 v2

Authors: Wojciech Matysiak , Paweł J. Szabłowski

Abstract

Existence, $L^2$ -stationarity and linearity of conditional expectations $\wwo{X_k}{...,X_{k-2},X_{k-1}}$ of square integrable random sequences $\mathbf{X}=(X_{k})_{k\in\mathbb{Z}}$ satisfying $\wwo{X_k}{...,X_{k-2},X_{k-1},X_{k+1},X_{k+2},...}=\sum_{j=1}^\infty b_j(X_{k-j}+X_{k+j})$ for a real sequence $(b_n)_{n\in\nat}$ , is examined. The analysis is reliant upon the use of Laurent and Toeplitz operator techniques.

Keywords

operator theory

Cite

@article{arxiv.math/0507332,
  title  = {Generalized stationary random fields with linear regressions - an operator approach},
  author = {Wojciech Matysiak and Paweł J. Szabłowski},
  journal= {arXiv preprint arXiv:math/0507332},
  year   = {2011}
}

Comments

The current, final version of the paper has a slightly different title (the previous title was "Non-Markov random fields with linear regressions -- a Toeplitz operators approach")

Generalized stationary random fields with linear regressions - an operator approach

Abstract

Keywords

Cite

Comments

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