Related papers: First order statistic of afterpulsing and crosstal…

The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the…

A particle entering a scattering and absorbing medium executes a random walk through a sequence of scattering events. The particle ultimately achieves first-passage, leaving the medium or it is absorbed. The Kubelka-Munk model describes a…

In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or…

In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time…

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this…

Within the framework of the random first-order transition theory of glasses, we discuss the statistics of thermal avalanches, the large scale rearrangements in driven amorphous systems near their instability. Stringy excitations yield…

Bootstrap percolation transition may be first order or second order, or it may have a mixed character where a first order drop in the order parameter is preceded by critical fluctuations. Recent studies have indicated that the mixed…

The waiting time distribution has, in recent years, proven to be a useful statistical tool for characterising transport in nanoscale quantum transport. In particular, as opposed to moments of the distribution of transferred charge, which…

An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…

Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian)…

A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…

In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…

The statistics of charge transport across a tunnel junction with energy-dependent scattering is investigated. A model with quadratic dispersion relation is discussed in general and, independently, in the two limiting cases of a large…

The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in…

Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean…

The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…

We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…

We consider a collection of independent standard Brownian particles (or random walks), starting from a configuration where at least one particle is positive, and study the first time they all become negative. This is clearly equivalent to…

Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…

Process mining starts from event data. The ordering of events is vital for the discovery of process models. However, the timestamps of events may be unreliable or imprecise. To further complicate matters, also causally unrelated events may…