Related papers: Targets and Holes
We obtain error terms on the rate of convergence to Extreme Value Laws for a general class of weakly dependent stochastic processes. The dependence of the error terms on the `time' and `length' scales is very explicit. Specialising to data…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
We investigate the scaling of the escape rate from piecewise-linear dynamical systems displaying intermittency due to the presence of an indifferent fixed-point. Strong intermittent behaviour in the dynamics can result in the system…
A natural question of how the survival probability depends upon a position of a hole was seemingly never addressed in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related…
The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non periodic points. Then we build a general…
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one…
The extremal index is a quantity introduced in extreme value theory to measure the presence of clusters of exceedances. In the dynamical systems framework, it provides important information about the dynamics of the underlying systems. In…
We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and H\"older potentials. For small holes, we show that a large class of initial distributions share the…
The extreme values theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological…
This paper studies finite-time safety and reach-avoid verification for stochastic discrete-time dynamical systems. The aim is to ascertain lower and upper bounds of the probability that, within a predefined finite-time horizon, a system…
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…
Introducing the concept of the extreme trapping horizon, we discuss geometric features of dynamical extreme black holes in four dimensions and then derive the integral identities which hold for the dynamical extreme black holes. We address…
We study a single risky financial asset model subject to price impact and transaction cost over an finite time horizon. An investor needs to execute a long position in the asset affecting the price of the asset and possibly incurring in…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
We study the escape rate for the Farey map, an infinite measure preserving system, with a hole including the indifferent fixed point. Due to the ergodic properties of the map, the standard theoretical approaches to this problem cannot be…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
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 apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage…