Renewal processes based on generalized Mittag–Leffler waiting times

Waiting times and Generalized Fibonacci Sequences

Waiting times for M / M systems under generalized processor sharing

We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system. We derive systems of ordinary differential equations fo...

Asymptotic Recurrence and Waiting times for Stationary Processes

Let X = fX n ; n 2 Zg be a discrete-valued stationary ergodic process distributed according to P and let x = of the recurrence time R n deened as the rst time that the initial n-block x n 1 = (x 1 ; x 2 ; : : : ; x n) reappears in the past of x. We identify an associated random walk, ? log P (X n 1); on the same probability space as X, and we prove a strong approximation theorem between log R n...

Anomalous processes with general waiting times: functionals and multipoint structure.

Many transport processes in nature exhibit anomalous diffusive properties with nontrivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtu...

Relative entropy and waiting times for continuous-time Markov processes

For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one does need a reference measure and so the natural object is relative entropy rather than entropy. In this paper we elaborate on this in the case of continuous-t...