Motivated by non-Poisson stochastic variability found in service system arrival data, we extend established service system staffing algorithms using the square-root staffing formula to allow for non-Poisson arrival processes. We develop a general model of the non-Poisson non-stationary arrival process that includes as a special case the non-stationary Cox process (a modification of a Poisson pr...

We study the sample autocovariance and autocorrelation function of the stationary AR(1) process with ARCH(1) errors. In contrast to ARCH and GARCH processes, AR(1) processes with ARCH(1) errors can not be transformed into solutions of linear stochastic recurrence equations. However, we show that they still belong to the class of stationary sequences with regular varying nite-dimensional distrib...

Multivariate Lévy-driven mixed moving average (MMA) processes of the type Xt = ∫ ∫ f(A, t − s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) CARMA processes and increments of fractional Lévy processes. In this paper, we introduce multivariate MMA pro...

The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afford both mathematical simplicity and algorithmic efficiency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic represent...

The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afford both mathematical simplicity and algorithmic efficiency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic represent...

We study a random process with reinforcement, which evolves following the dynamics of given diffusion in bounded domain and is resampled according to its occupation measure when it reaches boundary. show that converges unique quasi-stationary distribution absorbed at boundary domain. Our proofs use recent results theory distributions stochastic approximation techniques.

This paper presents a method to analyze the transitory response of complex and nonlinear systems, which are excited by non-Gaussian and non-stationary random fields, by solving of a statistical inverse problem with experimental measurements. Based on a double expansion, it is particularly adapted to the modeling of stochastic processes that are only characterized by a relatively small set of in...

Consider a stochastic process {x(t), t€T} of random elements of a Hilbert space H, whose index set is a locally compact Hausdorff space. The results obtained in this work fall into two broad categories, first the study of weakly stationary processes and their representations, and secondly the study of the sample path properties of not necessarily . stationary processes. In each case, we choose ...