Page 1

Displaying 1 – 8 of 8

Showing per page

Bernstein inequality for the parameter of the pth order autoregressive process AR(p)

Samir Benaissa (2006)

Applicationes Mathematicae

The autoregressive process takes an important part in predicting problems leading to decision making. In practice, we use the least squares method to estimate the parameter θ̃ of the first-order autoregressive process taking values in a real separable Banach space B (ARB(1)), if it satisfies the following relation: X ̃ t = θ ̃ X ̃ t - 1 + ε ̃ t . In this paper we study the convergence in distribution of the linear operator I ( θ ̃ T , θ ̃ ) = ( θ ̃ T - θ ̃ ) θ ̃ T - 2 for ||θ̃|| > 1 and so we construct inequalities of Bernstein type for this operator.

Block distribution in random strings

Peter J. Grabner (1993)

Annales de l'institut Fourier

For almost all infinite binary sequences of Bernoulli trials ( p , q ) the frequency of blocks of length k ( N ) in the first N terms tends asymptotically to the probability of the blocks, if k ( N ) increases like log 1 p N - log 1 p N - ψ ( N ) (for p q ) where ψ ( N ) tends to + . This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case p = q = 1 2 .

Borel methods of summability and ergodic theorems

Ryszard Jajte (2002)

Annales Polonici Mathematici

Passing from Cesàro means to Borel-type methods of summability we prove some ergodic theorem for operators (acting in a Banach space) with spectrum contained in ℂ∖(1,∞).

Currently displaying 1 – 8 of 8

Page 1