Generalized stationary random fields with linear regressions - an operator approach
Abstract
Existence, L2-stationarity and linearity of conditional expectations Xk...,Xk-2,Xk-1 of square integrable random sequences X=(Xk)k∈Z satisfying \[ Xk...,Xk-2,Xk-1,Xk+1,Xk+2,...=Σj=1∞ bj(Xk-j+Xk+j) \] for a real sequence (bn)n∈, is examined. The analysis is reliant upon the use of Laurent and Toeplitz operator techniques.
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