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We establish sufficient conditions for the existence, and derive explicit formulas for the $\kappa$'th moments, $\kappa \geq 1$, of Markov modulated generalized Ornstein-Uhlenbeck processes as well as their stationary distributions. In…
This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…
In this paper we extend the predicate logic introduced in [Beauquier et al. 2002] in order to deal with Semi-Markov Processes. We prove that with respect to qualitative probabilistic properties, model checking is decidable for this logic…
This is a survey of old and new problems and results in additive number theory.
A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…
We prove an invariance principle (functional central limit theorem) for a vector-valued additive functional of a Markov chain for almost every starting point with respect to an ergodic equilibrium distribution. The hypothesis is a moment…
Comparison results for Markov processes w.r.t. function class induced (integral) stochastic orders have a long history. The most general results so far for this problem have been obtained based on the theory of evolution systems on Banach…
We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
Calculating the spectral function of two dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two dimensional…
A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track…
In this paper, a fourth moment bound for partial sums of functional of strongly ergodic Markov chain is established. This type of inequality plays an important role in the study of empirical process invariance principle. This one is…
For non-equilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any…
Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniqueness of such solutions, as well as for continuous dependence…
The idea of the restricted mean has been used to establish a significantly improved version of Markov's inequality that does not require any new assumptions. The result immediately extends on Chebyshev's inequalities and Chernoff's bound.…
In the article the distributions of overjump functionals for almost semi-continuous processes on a finite irreducible Markov chain are considered.
Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…
We consider a class of finite Markov moment problems with arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the non-unique solution families.…