Matrix variate distributions are are used to quantify uncertainty in the mass, stiffness and damping matrices. The proposed approach is based on the so called Wishart random matrices. The probability density function of the system matrices are derived using the maximum entropy method. It is assumed that the mean of the system matrices are known. A new optimal Wishart distribution is proposed to...

We consider increasing self–similar Markov processes (Xt, t ≥ 0) on ]0,∞[. By using the Lamperti’s bijection between self–similar Markov processes and Lévy processes, we determine the functions f for which there exists a constant c ∈ R+ \{0} such that lim inft→∞Xt/f(t) = c with probability 1. The determination of such functions depends on the subordinator ξ associated to X through the distribut...

With any max-stable random process η on X = Zd or Rd, we associate a random tessellation of the parameter space X . The construction relies on the Poisson point process representation of the max-stable process η which is seen as the pointwise maximum of a random collection of functions Φ = {φi, i ≥ 1}. The tessellation is constructed as follows: two points x, y ∈ X are in the same cell if and o...

We consider a birth-death process {X(t), t ≥ 0} on the positive integers for which the origin is an absorbing state with birth coefficients λn, n ≥ 0 and death coefficients μn, n ≥ 0. We recall that the series A = ∑∞ n=1 1 λnπn and the series S = ∑∞ n=1 1 λnπn ∑∞ i=n+1 πi, where {πn, n ≥ 1} is the potential coefficients. It is well-known fact (see van Doorn [13]) that if the A = ∞ and S < ∞, th...

We present a new, partial order planner called PSIPLAN, which builds on SNLP. We drop the closed world assumption, add sensing actions, "~ld a class of propositions about the agent’s knowledge, and add a class of universally quantified propositions. This latter class of propositions, which we call C-forms, distinguishes this research. ~,-forms represent partially closed worlds, such as "’Block ...

Abstract. In this article we prove a local large deviation principle (LLDP) for the critical multitype Galton-Watson process from spectral potential point. We define the so-called a spectral potential UK( ·, π) for the Galton-Watson process, where π is the normalized eigen vector corresponding to the leading Perron-Frobenius eigen value 1l of the transition matrix A(·, ·) defined from K, the tr...

This paper is concerned with a compositional approach for constructing infinite abstractions of interconnected discrete-time stochastic control systems. The proposed approach uses the interconnection matrix and joint dissipativity-type properties of subsystems and their abstractions described by a new notion of so-called stochastic storage functions. The interconnected abstraction framework is ...