Bornes pour la distribution limite de la statistique de Shepp
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...
We investigate properties of harmonic functions of the symmetric stable Lévy process on 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...
We extend some recent work of S. Y. Chang, J. M. Wilson and T. Wolff to the bidisc. For , we determine the sharp order of local integrability obtained when the square function of is in . 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 in .
Let be a fixed point of a substitution on the alphabet and let and . We give a complete classification of the substitutions according to whether the sequence of matrices is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.
Stochastic Petri nets generalize the notion of queuing systems and are a useful model in performance evaluation of parallel and distributed systems. We give necessary and sufficient conditions for the boundedness of a stochastic process related to these nets.
This paper uses the Rice method [18] to give bounds to the distribution of the maximum of a smooth stationary Gaussian process. We give simpler expressions of the first two terms of the Rice series [3,13] for the distribution of the maximum. Our main contribution is a simpler form of the second factorial moment of the number of upcrossings which is in some sense a generalization of Steinberg et al.'s formula ([7] p. 212). Then, we present a numerical application and asymptotic expansions...