Displaying similar documents to “Improvement of prediction for a larger number of steps in discrete stationary processes”

Non-negative linear processes

Martin Anděl (1991)

Applications of Mathematics

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Conditions under which the linear process is non-negative are investigated in the paper. In the definition of the linear process a strict white noise is used. Explicit results are presented also for the models AR(1) and AR(2).

On the representation of functions by orthogonal series in weighted L p spaces

M. Grigorian (1999)

Studia Mathematica

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It is proved that if φ n is a complete orthonormal system of bounded functions and ɛ>0, then there exists a measurable set E ⊂ [0,1] with measure |E|>1-ɛ, a measurable function μ(x), 0 < μ(x) ≤ 1, μ(x) ≡ 1 on E, and a series of the form ∑ k = 1 ∞ c k φ k ( x ) , where c k ∈ l q for all q>2, with the following properties: 1. For any p ∈ [1,2) and f ∈ L μ p [ 0 , 1 ] = f : ʃ 0 1 | f ( x ) | p μ ( x ) d x < ∞ there are numbers ɛ k , k=1,2,…, ɛ k = 1 or 0, such that l i m n → ∞ ʃ 0 1 | ∑ k = 1 n ɛ k c k φ k ( x ) - f ( x ) | p μ ( x ) d x = 0 . 2. For every p ∈ [1,2) and f ∈ L μ p [ 0 , 1 ] there are a function g ∈ L 1 [ 0 , 1 ] with g(x) = f(x) on E and numbers δ k , k=1,2,…, δ k = 1 or 0,...