We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x, σ) ∈ Ω × Γ, Ω being a region in R or the d–dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully–coupled. We study st...

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian SIS process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infection rate exceeds 1/ ln(λ1 + 1), whe...

This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative functional of X. A key result is the uniqueness theorem for a positive eigenfunction of the pricing ...

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian susceptible-infected-susceptible (SIS) process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infect...

A Markovian Petri net is a stochastic discrete event system frequently used for analysis and performance evaluation purposes. In the past, the fluidification has been proposed as a relaxation technique for avoiding the ”state explosion problem”. Following the same approach, in this paper a hybrid Petri net model is defined as a partial relaxation of an original Markovian Petri net. It is shown ...

We consider a finite-buffer single server queueing system with queue-length dependent vacations where arrivals occur according to a batch Markovian arrival process (BMAP). The service discipline is P-limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of L customers has been served. Depending on ...

This paper studies an infinite-server queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates λi by a factor N , tail probabilities are examined when letting N tend to∞; non-standard large deviations results are obtained. An importance-sampling based estimation algori...

Statistical evidence suggests that the autocorrelation function (k) (k = 0; 1; : : :) of a compressed-video sequence is better captured by (k) = e ? p k than by (k) = k ? = e ? log k (long-range dependence) or (k) = e ?k (Markovian). A video model with such a correlation structure is introduced based on the so-called M jGj1 input processes. In essence, the M jGj1 process is a stationary version...

In this paper we introduce the adaptive MMAP[K] arrival process and analyze the adaptive MMAP[K]/PH[K]/1 queue. In such a queueing system, customers of K different types with Markovian inter-arrival times and possibly correlated customer types, are fed to a single server queue that makes use of r thresholds. Service times are phase-type and depend on the type of customer in service. Type k cust...