Properties of the Wold Decomposition of Stationary Stochastic Processes
Enders Anthony Robinson · Theory of Probability and Its Applications · 1963
The basic results of the paper (Theorems 11–13) treat the representation of the quantities $\hat x_{t + \alpha } $ – the best predictors of the quantities $x_{t + \alpha } $ of a process, which is stationary in the wide sense, from the quantities $x_s , s \leqq t$ – in the form of a series \[ \hat x_{t + \alpha } \sim \sum\limits_{s = 0}^\infty {k_s x_{t - s} } ,\]where the coefficients ${k_s }$ satisfy the condition $\sum |k_s |^2 < \infty $. Certain properties of the sequences $\{ w_t \} \sum ,{|w_t |}^2 < \infty $, are derived first.