In many chronic conditions, subjects alternate between an active and an inactive state, and sojourns into the active state may involve multiple lesions, infections, or other recurrences with different times of onset and resolution. We present a biologically interpretable model of such chronic recurrent conditions based on a queueing process. The model has a birth-death process describing recurr...

A classical random walk (St, t ∈ N) is defined by St := t ∑ n=0 Xn, where (Xn) are i.i.d. When the increments (Xn)n∈N are a one-order Markov chain, a short memory is introduced in the dynamics of (St). This so-called “persistent” random walk is nolonger Markovian and, under suitable conditions, the rescaled process converges towards the integrated telegraph noise (ITN) as the time-scale and spa...

In this paper we extend the predicate logic introduced in [BRS02] in order to deal with Semi-Markov Processes. We prove that with respect to qualitative probabilistic properties, model checking is decidable for this logic applied to Semi-Markov Processes. Furthermore we apply our logic to Probabilistic Timed Automata considering classical and urgent semantics, and considering also predicates on...

Abstract: Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of R. Pyke and R. Schaufele (1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example in finance and insurance. Unfortunately, no limit theorems have been ...

Statistical complexity is a measure of complexity of discrete-time stationary stochastic processes, which has many applications. We investigate its more abstract properties as a non-linear function of the space of processes and show its close relation to the Knight’s prediction process. We prove lower semi-continuity, concavity, and a formula for the ergodic decomposition of statistical complex...

We described semi-Markov models which relaxes usual Markov assumptions made in hidden Markov models. Semi-Markov models classify segments of adjacent words, rather than single words. We proposed two training strategies, a discriminative training and a generative training for semi-Markov models. Importantly, features for semi-Markov models can measure properties of segments, and transitions with...