Related papers: How close are time series to power tail L\'evy dif…
We consider a Markovian load balancing model on a fully-connected network, where calls have Poisson arrivals and exponential durations. The endpoints of each call are uniform over all the links of the network. Each call is routed either…
Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative…
We study optimal Markovian couplings of Markov processes, where the optimality is understood in terms of minimization of concave transport costs between the time-marginal distributions of the coupled processes. We provide explicit…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
We consider a Markov process $X$, which is the solution of a stochastic differential equation driven by a L\'{e}vy process $Z$ and an independent Wiener process $W$. Under some regularity conditions, including non-degeneracy of the…
The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of…
We study the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. By a coupling approach, we establish global contraction in an $L^1$ Wasserstein…
The L\'evy walk is a non-Brownian random walk model that has been found to describe anomalous dynamic phenomena in diverse fields ranging from biology over quantum physics to ecology. Recurrently occurring problems are to examine whether…
In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We…
Methodologies to test hypotheses about the tail-heaviness of an underlying distribution are introduced based on results of Rojo (1996) using the limiting behavior of the extreme spacings. The tests are consistent and have point-wise robust…
We study a real-valued L\'evy-type process $X$, which is locally $\alpha$-stable in the sense that its jump kernel is a combination of a `principal' (state dependent) $\alpha$-stable part with a `residual' lower order part. We show that…
An aperiodic and irreducible Markov chain on a finite state space converges to its stationary distribution. When convergence to equilibrium is measured by total variation distance, there exists an optimal coupling and a maximal coupling…
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
Extreme events are by nature rare and difficult to predict, yet are often much more important than frequent, typical events. An interesting counterpoint to the prediction of such events is their retrodiction -- given a process in an outlier…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
Rare events in stochastic processes with heavy-tailed distributions are controlled by the big jump principle, which states that a rare large fluctuation is produced by a single event and not by an accumulation of coherent small deviations.…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…