We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurement of the process only at integer times. We then construct a specific sequence for which the per...

For a multidimensional Itô process (Xt)t≥0 driven by a Brownian motion, we are interested in approximating the law of ψ ( (Xs)s∈[0,T ] ) , T > 0 deterministic, for a given functional ψ using a discrete sample of the process X. For various functionals (related to the maximum, to the integral of the process, or to the killed/stopped path) we extend to the non Markovian framework of Itô processes ...

Keywords: Queueing Tandem queueing system Marked Markovian arrival process Phase-type distribution Laplace–Stieltjes transform a b s t r a c t A tandem queueing system with infinite and finite intermediate buffers, heterogeneous customers and generalized phase-type service time distribution at the second stage is investigated. The first stage of the tandem has a finite number of servers without...

We consider the estimation of hidden Markovian process by using information geometry with respect to transition matrices. We consider the case when we use only the histogram of k-memory data. Firstly, we focus on a partial observation model with Markovian process and we show that the asymptotic estimation error of this model is given as the inverse of projective Fisher information of transition...

A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary nonexponential distribution of the residence times, is developed. The formally exact expression for the Laplace-transformed quantum propagator averaged over the stationary realizations of such N -state non-Markovian noise is obtained. The theory possesse...

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. W...

Numerous applications all theway frombiology and physics to economics depend on the density of first crossings over a boundary.Motivated by the lack of general purpose analytical tools for computingfirst-passage time densities (FPTDs) for complex problems, we propose a new simple method based on the independent interval approximation (IIA).We generalise previous formulations of the IIA to inclu...

A number of Bayesian tracking models involve auxiliary discrete variables beside the main hidden state of interest. These discrete variables usually follow a Markovian process and interact with the hidden state either via its evolution model or via the observation process, or both. We consider here a general model that encompasses all these situations, and show how Bayesian filtering can be rig...