We clarify some ways in which wavelet-based synthesis of fractional Brownian motion is used and can be useful. In particular, we examine the choice of an initial scale in the waveletbased synthesis method, compare it to other methods for simulation of fractional Brownian motion, and discuss connections to strong invariance principles encountered in Probability and Statistics.

The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the Lévy stable distributions, and more generally the probability distributions governed by generalized diffusion equations of fractional order in space and/or in time. In these cases the related stochast...

In this paper, two learning automata based adaptive limited fractional guard channel algorithms for cellular mobile networks are proposed. These algorithms try to minimize the blocking probability of new calls subject to the constraint on the dropping probability of the handoff calls. To evaluate the proposed algorithms, computer simulation are conducted. The simulation results show that the pe...

We study a family of importance sampling estimators for the problem of computing the probability of level crossing when the crossing level is large, or when the intensity of the noise is small. We give general results concerning centered gaussian processes with drift and develop a method which allows to compute explicitly the asymptotics of the second order moment, with a special mention for th...

We consider a system of d non-linear stochastic fractional heat equations in spatial dimension 1 driven by multiplicative d-dimensional space–time white noise. establish sharp Gaussian-type upper bound on the two-point probability density function (u(s,y),u(t,x)). From this result, we deduce optimal lower bounds hitting probabilities process {u(t,x):(t,x)?[0,?[×R} non-Gaussian case, terms Newto...

The Fokker-Planck equation is considered, which is connected to the birth and death process with immigration by the Poisson transform. The fractional derivative in time variable is introduced into the Fokker-Planck equation in order to investigate an origin of oscillatory behavior of cumulant moments. From its solution (the probability density function), the generating function (GF) for the cor...

Extending the notion of (random) k-out graphs, we consider when the k-out hypergraph is likely to have a perfect fractional matching. In particular, we show that for each r there is a k = k(r) such that the k-out r-uniform hypergraph on n vertices has a perfect fractional matching with high probability (i.e., with probability tending to 1 as n → ∞) and prove an analogous result for r-uniform r-...