Related papers: A L\'{e}vy input model with additional state-depen…
We study a many-server queuing system with general service time distribution and state dependent service rates. The dynamics of the system are modeled using measure valued processes which keep track of the residual service times. Under…
The $q-$state clock model, sometimes called the discrete $XY$ model, is known to show a second-order (symmetry breaking) phase transition in two-dimension (2D) for $q\le 4$ ($q=2$ corresponds to the Ising model). On the other hand, the…
We propose a unified stochastic SIR model driven by L\'{e}vy noise. The model is structural enough to allow for time-dependency, nonlinearity, discontinuity, demography and environmental disturbances. We present concise results on the…
Let $\{D(s), s \geq 0\}$ be a non-decreasing L\'evy process. The first-hitting time process $\{E(t) t \geq 0\}$ (which is sometimes referred to as an inverse subordinator) defined by $E(t) = \inf \{s: D(s) > t \}$ is a process which has…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
It is known that the exponential functional of a Poisson process admits a probability density function in the form of an infinite series. In this paper, we obtain an explicit expression for the density function of the exponential functional…
We derive a small-time expansion for out-of-the-money call options under an exponential Levy model, using the small-time expansion for the distribution function given in Figueroa-Lopez & Houdre (2009), combined with a change of num\'eraire…
We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth and death like transitions, for which it is shown that for any state $i$, the rate of two…
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 discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
We develop a predictor-feedback control design for a class of linear systems with state-dependent switching. The main ingredient of our design is a novel construction of an exact predictor state. Such a construction is possible as for a…
Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much…
We consider a L\'evy process reflected at the origin with additional i.i.d. collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study…
In a rather general setting of It\^o-L\'evy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such…
In this paper, we study the L\'evy process time-changed by independent L\'evy subordinators, namely, the incomplete gamma subordinator, the $\epsilon$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive…
We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or…
We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue in a different way. Inter-event times in all models are Mittag-Leffler distributed, which is a heavy tail distribution with no…
In this paper, we solve exit problems for a level-dependent L\'evy process which is exponentially killed with a killing intensity that depends on the present state of the process. Moreover, we analyse the respective resolvents. All…
Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length distribution, which is not addressed in [1]. In this paper,…