Related papers: Hitting Time Statistics and Extreme Value Theory

Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite…

In this paper we study the quenched distributions of hitting times for a class of random dynamical systems. We prove that hitting times to dynamically defined cylinders converge to a Poisson point process under the law of random equivariant…

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to…

We study rare events in the extreme value statistics of stochastic symmetric jump processes with power tails in the distributions of the jumps, using the big-jump principle. The principle states that in the presence of stochastic processes…

Nerve transmission delay is an important topic in neuroscience. Spike signals fired or received at the dendrites of a neuron travel from the axon to the presynaptic cell. The spike signal triggers a chemical reaction at the synapse, wherein…

We consider the hard-core model with Metropolis transition probabilities on finite grid graphs and investigate the asymptotic behavior of the first hitting time between its two maximum-occupancy configurations in the low-temperature regime.…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description…

Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special…

Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However,…

This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its…

This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of…

Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…

We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process:…

The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…

Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…

We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…