A few remarks on Bryc's paper on 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.

A Few Remarks on Linear Forms Involving Catalan’s Constant

Abstract. In the joint work [RZ] of T. Rivoal and the author, a hypergeometric construction was proposed for studing arithmetic properties of the values of Dirichlet’s beta function β(s) at even positive integers. The construction gives some bonuses [RZ], Section 9, for Catalan’s constant G = β(2), such as a second-order Apéry-like recursion and a permutation group in the sense of G. Rhin and C...

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.

A Few Remarks on Algorithmic Composition