Stationary random fields with linear regressions

Stationary random fields with linear regressions ∗

We analyze and identify stationary fields with linear regressions and quadratic conditional variances. We give sufficient conditions to determine one dimensional distributions uniquely as normal, and as certain compactly-supported distributions. Our technique relies on orthogonal polynomials, which under our assumptions turn out to be a version of the so called continuous q-Hermite polynomials.

Generalized Stationary Random Fields with Linear Regressions - an Operator Approach

Existence, L-stationarity and linearity of conditional expectations E [ Xk ∣. . . , Xk−2, Xk−1 ] of square integrable random sequences X = (Xk)k∈Z satisfying E [ Xk ∣. . . , Xk−2, Xk−1, Xk+1, Xk+2, . . . ] = ∞ ∑ j=1 bj ( Xk−j + Xk+j ) for a real sequence (bn)n∈N, is examined. The analysis is reliant upon the use of Laurent and Toeplitz operator techniques.

Stationary Markov chains with linear regressions

In Bryc(1998) we determined one dimensional distributions of a stationary field with linear regressions (1) and quadratic conditional variances (2) under a linear constraint (7) on the coefficients of the quadratic expression (3). In this paper we show that for stationary Markov chains with linear regressions and quadratic conditional variances the coefficients of the quadratic expression are i...

Kernel density estimation for stationary random fields

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Transformations of random regressions