Related papers: Interevent time distribution in seismicity: a theo…
The empirical Bath's law is derived from the magnitude-difference statistical distribution of earthquake pairs. The pair distribution related to earthquake correlations is presented. The single-event distribution of dynamically correlated…
When we quantize a system consisting of a single particle, the proper time $\tau $ and the rest mass $m$ are usually dealt with as parameters. In the present article, however, we introduce a new quantization rule by which these quantities…
We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of…
A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…
In this paper, we study a distributed parameter estimation problem with an asynchronous communication protocol over multi-agent systems. Different from traditional time-driven communication schemes, in this work, data can be transmitted…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…
We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate…
Processes involving bursts of activity separated by quiescent periods occur across diverse systems and scales. In human dynamics, these phenomena have been described by power-law inter-event time distributions, $P(t)\sim t^{-\alpha}$, with…
The dynamics of electronic tunneling through a disordered 1D chain of finite length is considered. We calculate distributions of the transmission coefficient T, Wigner delay time and, $\tau_\phi$ and the transport time, $\tau_t=T\tau_\phi$.…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
Rainfall exhibits extreme variability at many space and time scales and calls for a statistical description. Based on an analysis of radar measurements of precipitation over the tropical oceans, we introduce a new probability law for the…
In many important systems exhibiting crackling noise --- intermittent avalanche-like relaxation response with power-law and, thus, self-similar distributed event sizes --- the "laws" for the rate of activity after large events are not…
We study statistical distributions in a mechanical model for an earthquake fault introduced by Burridge and Knopoff [R. Burridge and L. Knopoff, {\sl Bull. Seismol. Soc. Am.} {\bf 57}, 341 (1967)]. Our investigations on the size (moment),…
We use the two-time scale subordination in order to describe dynamical processes in continuous media with a long-term memory. Our consideration touches two physical examples in detail. First we study a temporal evolution of the species…
We develop a general theory of the time distribution of quantum events, applicable to a large class of problems such as arrival time, dwell time and tunneling time. A stopwatch ticks until an awaited event is detected, at which time the…
The spatial distribution of persistent (unvisited) sites in one dimensional $A+A\to\emptyset$ model is studied. The `empty interval distribution' $n(k,t)$, which is the probability that two consecutive persistent sites are separated by…
Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…