Related papers: Transient analysis of a stationary L\'evy-driven q…

For spectrally positive L\'evy processes killed on exiting the half-line, existence of a quasi-stationary distribution is characterized by the exponential integrability of the exit time, the Laplace exponent and the non-negativity of the…

We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…

We consider a tandem queue with coupled processors, which is subject to global breakdowns. When the network is in the operating mode and both queues are non empty, the total service capacity is shared among the stations according to fixed…

The notion of degree and related notions concerning recurrence and transience for a class of L'evy processes on metric Abelian groups are studied. The case of random walks on a hierarchical group is examined with emphasis on the role of the…

Let $\{D(s), s \geq 0 \}$ be a L\'evy subordinator, that is, a non-decreasing process with stationary and independent increments and suppose that $D(0) = 0$. We study the first-hitting time of the process $D$, namely, the process $E(t) =…

We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…

Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.

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…

We study long time behavior of integrated trawl processes introduced by Barndorff-Nielsen. The trawl processes form a class of stationary infinitely divisible processes, described by an infinitely divisible random measure (L\'evy base) and…

In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…

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…

We show on- and off-diagonal upper estimates for the transition densities of symmetric Levy and Levy-type processes. To get the an-diagonal estimates we prove a Nash type inequality for the related Dirichlet form. For the off-diagonal…

For a spectrally one-sided L\'{e}vy process, we extend various two-sided exit identities to the situation when the process is only observed at arrival epochs of an independent Poisson process. In addition, we consider exit problems of this…

We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Amongst others, we study cases where the interarrival and service times are proportionally dependent with additive and/or subtracting…

We consider the class of (possibly killed) spectrally positive L\'evy process that have been time-changed by the inverse of an integral functional. Within this class we characterize the family of those processes which satisfy the following…

We consider queueing output processes of some elementary queueing models such as the M/M/1/K queue and the M/G/1 queue. An important performance measure for these counting processes is their variance curve, indicating the variance of the…

This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we…

The transient response of a stationary state of a quantum particle in a step potential to an instantaneous change in the step height (a simplified model for a sudden bias switch in an electronic semiconductor device) is solved exactly by…

This paper provides rate-efficient estimators of the volatility parameter in the presence of L\'{e}vy jumps