Diskrete, mittelbare Gruppen.
Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [R. Abraham and L. Serlet, Elect. J. Probab. 7 (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, Probab. Th....
Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [R. Abraham and L. Serlet, Elect. J. Probab.7 (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, Probab. Th....
Recently the renormalization group predictions on the effect of disorder on pinning models have been put on mathematical grounds. The picture is particularly complete if the disorder is relevant or irrelevant in the Harris criterion sense: the question addressed is whether quenched disorder leads to a critical behavior which is different from the one observed in the pure, i.e. annealed, system. The Harris criterion prediction is based on the sign of the specific heat exponent of the pure system,...
We study the continuous time version of the random walk pinning model, where conditioned on a continuous time random walk (Ys)s≥0 on ℤd with jump rate ρ > 0, which plays the role of disorder, the law up to time t of a second independent random walk (Xs)0≤s≤t with jump rate 1 is Gibbs transformed with weight eβLt(X,Y), where Lt(X, Y) is the collision local time between X and Y up to time t. As the inverse temperature β varies, the model undergoes a localization–delocalization transition at...
Generalizations of the hazard functions are proposed and general hazard rate orders are introduced. Some stochastic orders are defined as general ones. A unified derivation of relations between the dispersive order and some other orders of distributions is presented
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all.The main tool used is the duality between risk-sensitive integrals and relative entropy, and we...
We elucidate the asymptotics of the Ls-quantization error induced by a sequence of Lr-optimal n-quantizers of a probability distribution P on when s > r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s < r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.
For a doubly truncated exponential distribution, the probability density function of a quasi-range is derived. From this the density of sample range is obtained as a special case. Expressions for the mean and variance of the range are also obtained.
Se analizan los conceptos de función de distribución propensa, neutra y resistente a producir datos atípicos dependiendo del comportamiento asintótico de la diferencia y la razón de los dos extremos superiores.Posteriormente se caracterizan las primeras definiciones con propiedades de la cola derecha de la función de distribución.
We prove good- inequalities for the area integral, the nontangential maximal function, and the maximal density of the area integral. This answers a question raised by R. F. Gundy. We also prove a Kesten type law of the iterated logarithm for harmonic functions. Our Theorems 1 and 2 are for Lipschitz domains. However, all our results are new even in the case of .