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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,∞).

Bottom-up modeling of domestic appliances with Markov chains and semi-Markov processes

Rajmund Drenyovszki, Lóránt Kovács, Kálmán Tornai, András Oláh, István Pintér (2017)

Kybernetika

In our paper we investigate the applicability of independent and identically distributed random sequences, first order Markov and higher order Markov chains as well as semi-Markov processes for bottom-up electricity load modeling. We use appliance time series from publicly available data sets containing fine grained power measurements. The comparison of models are based on metrics which are supposed to be important in power systems like Load Factor, Loss of Load Probability. Furthermore, we characterize...

Boundary potential theory for stable Lévy processes

Paweł Sztonyk (2003)

Colloquium Mathematicae

We investigate properties of harmonic functions of the symmetric stable Lévy process on ℝ d without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman-Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for...

Bounded double square functions

Jill Pipher (1986)

Annales de l'institut Fourier

We extend some recent work of S. Y. Chang, J. M. Wilson and T. Wolff to the bidisc. For f ∈ L l o c 1 ( R 2 ) , we determine the sharp order of local integrability obtained when the square function of f is in L ∞ . The Calderón-Torchinsky decomposition reduces the problem to the case of double dyadic martingales. Here we prove a vector-valued form of an inequality for dyadic martingales that yields the sharp dependence on p of C p in ∥ f ∥ p ≤ C p ∥ S f ∥ p .

Boundedness of oriented walks generated by substitutions

F. M. Dekking, Z.-Y. Wen (1996)

Journal de théorie des nombres de Bordeaux

Let x = x 0 x 1 ⋯ be a fixed point of a substitution on the alphabet a , b , and let U a = - 1 - 1 0 1 and U b = 1 1 0 1 . We give a complete classification of the substitutions σ : a , b ☆ according to whether the sequence of matrices U x 0 U x 1 ⋯ U x n n = 0 ∞ is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.

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