Related papers: On the relation between event-based and time-based…

We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

Statistical analysis on networks has received growing attention due to demand from various emerging applications. In dynamic networks, one of the key interests is to model the event history of time-stamped interactions amongst nodes. We…

Event attribution in the context of climate change seeks to understand the role of anthropogenic greenhouse gas emissions on extreme weather events, either specific events or classes of events. A common approach to event attribution uses…

For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model…

There are two main quantities involved in the deviation of a stochastic process from a Poisson process: the squared coefficient of variation of the time intervals between adjacent events and the Fano factor of the number of reaction events.…

Traditional reliability analysis has been using time to event data, degradation data, and recurrent event data, while the associated covariates tend to be simple and constant over time. Over the past years, we have witnessed the rapid…

A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…

We develop a comprehensive framework for analyzing full record statistics, covering record counts $M(t_1), M(t_2), \ldots$, and their corresponding attainment times $T_{M(t_1)}, T_{M(t_2)}, \ldots$, as well as the intervals until the next…

Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of…

The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…

In this paper, we propose a method for estimating the distribution of time differences between connected events (such as ad impressions and corresponding customer calls). A special feature of this method is that it does not require matching…

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…

In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly the system to the starting value. We analyze its relevant statistical properties like the transition probability and…

Event occurrence is not only subject to the environmental changes, but is also facilitated by the events that have occurred in a system. Here, we develop a method for estimating such extrinsic and intrinsic factors from a single series of…

Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.

Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…

Entries of datasets are often collected only if an event occurred: taking a survey, enrolling in an experiment and so forth. However, such partial samples bias classical correlation estimators. Here we show how to correct for such sampling…

In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…

The defining characteristic of event-based control is that feedback loops are only closed when indicated by a triggering condition that takes recent information about the system into account. This stands in contrast to periodic control…