We consider a stochastic process in a modified Ehrenfest urn model. The modification prescribes there to be a minimum number of balls in each urn, and the process records the differences between treatment assignments under a sampling scheme implemented with this modified Ehrenfest urn model. In contrast to the result that the difference process forms a Markov chain and converges to a stationary...

Non-stationary behavior of aggregated IP traffic patterns was demonstrated in a number of studies. However, none of those did either consider practical aspects of this phenomenon or propose suitable model to capture it. Searching for model for IP traffic aggregates we introduce the concept of local stationarity and demonstrate that it allows to model traffic patterns measured in high-speed oper...

Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt’s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrela...

Target tracking algorithms in radar systems have to operate in an environment of measurement uncertainty. A condition for good target tracking in a radar system is that a target position can be estimated and the measurement accuracy can be determined. The main problem is that clutter cannot be well defined by a stationary stochastic process and there is no known general model that works in diff...

In [11] an unusual connection between orthogonal polynomials and martingales has been studied. There, all orthogonal She er polynomials, were linked to a unique L evy process, i.e., a continuous time stochastic process with stationary and independent increments. The connection between the polynomials and the L evy process is expressed by a martingale relation. As an application of these marting...

This paper develops nonparametric tests of independence between two stationary stochastic processes. The testing strategy boils down to gauging the closeness between the joint and the product of the marginal stationary densities. For that purpose, I take advantage of a generalized entropic measure so as to build a class of nonparametric tests of independence. Asymptotic normality and local powe...

Let x(t) be a separable stationary normal stochastic process with zero mean, covariance function r(r) (with r(0) = 1, for convenience), and spectrum ^(X) having an absolutely continuous component. Let N denote the number of times x(t) crosses the zero level in Q^t^T and write X2 for the second spectral moment JQ\ dF(X) = —r"(0). Then it is well known that the mean of the random variable N is gi...

In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time. As the population evolves over time, the tree that represents the genealogy of the population also changes, leading to a tree-valued stochastic process known as the...

6 The zonally integrated meridional volume transport in the North Atlantic (called AMOC) 7 is described in a 19-year long ocean state estimate, one consistent with a diverse global data 8 set. Apart from a weak increasing trend at high northern latitudes, the AMOC appears 9 statistically stable over the last 19 years with fluctuations indistinguishable from those of 10 a stationary Gaussian sto...

Pickands constants play an important role in the exact asymptotic of extreme values for Gaussian stochastic processes. By the generalized Pickands constant Hη we mean the limit Hη = lim T→∞ Hη(T ) T , where Hη(T ) = IE exp ( maxt∈[0,T ] (√ 2η(t)− σ2 η(t) )) and η(t) is a centered Gaussian process with stationary increments and variance function σ2 η(t). Under some mild conditions on σ2 η(t) we ...