Related papers: A L\'evy input fluid queue with input and workload…
We introduce a framework and develop a theory of transitory queueing models. These are models that are not only non-stationary and time-varying but also have other features such as the queueing system operates over finite time, or only a…
Let $(Q_t)$ be a stationary workload process, and $r(t)$ the correlation coefficient of $Q_0$ and $Q_t$. In a series of previous papers (i) the transform of $r(\cdot)$ has been derived for the case that the driving process is…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
L\'evy processes, known for their ability to model complex dynamics with skewness, heavy tails and discontinuities, play a critical role in stochastic modeling across various domains. However, inference for most L\'evy processes, whether in…
We present a new form of intermittency, L\'evy on-off intermittency, which arises from multiplicative $\alpha$-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both…
We establish a connection between the scattering inverse problem and the determination of the distribution of the position of the Levy process at the exit time of a bounded interval in term of its Levy exponent.
Various recent results on quantum L\'evy processes are presented. The first part provides an introduction to the theory of L\'evy processes on involutive bialgebras. The notion of independence used for these processes is tensor…
This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…
Scheduling questions arise naturally in many different areas among which operating system design, compiling,... In real life systems, the characteristics of the jobs (such as release time and processing time) are usually unknown and…
This paper presents a new method for deriving the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive L\'evy input. The priority of a non-atomic customer (particle) is a function of their class…
In this paper, we consider the exponential functional \(A_{\infty}=\int_0^\infty e^{-\xi_s}ds\) of a L{\'e}vy process \(\xi_s\) and aim to estimate the characteristics of \(\xi_{s}\) from the distribution of \(A_{\infty}\). We present a new…
In this work we give a complete description to the asymptotic behaviors of exponential functionals of L\'evy processes and divide them into five different types according to their convergence rates. Not only their exact convergence speeds…
In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
This note considers the problem of statistical inference of the parameters of the input process to a queue from periodic workload observations. The main focus is the open problem of constructing statistically efficient estimators for a…
We investigate the work fluctuations in an overdamped non-equilibrium process that is stopped at a stochastic time. The latter is characterized by a first passage event that marks the completion of the non-equilibrium process. In…
A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of…
We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating…