Related papers: The effect of memory on functional large deviation…
We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show…
How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the…
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
Suppose $ E$ is a space with a null-recurrent Markov kernel $ P$. Furthermore, suppose there are infinite particles with variable weights on $ E$ performing a random walk following $ P$. Let $ X_{t}$ be a weighted functional of the position…
Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to…
In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large…
This paper describes limiting behaviour of tail empirical process associated with long memory stochastic volatility models. We show that such process has dichotomous behaviour, according to an interplay between a Hurst parameter and a tail…
We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…
This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy…
We consider the evolution of logistic maps under long-term memory. The memory effects are characterized by one parameter \alpha. If it equals to zero, any memory is absent. This leads to the ordinary discrete dynamical systems. For \alpha =…
Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory…
In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate…
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
A large deviations principle is established for the joint law of the empirical measure and the flow measure of a renewal Markov process on a finite graph. We do not assume any bound on the arrival times, allowing heavy tailed distributions.…
We obtain large deviations estimates for systems with stretched exponential decay of correlations, which improve the ones obtained in \cite{AFLV11}. As a consequence we obtain better large deviations estimates for Viana maps and get large…
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…