Related papers: Law Of Large Numbers For Random Dynamical Systems
In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance…
We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the…
This paper studies the counting problem in random dynamical systems. We noticed that the nature of counting in the random setting is completely different than that of the deterministic systems in the sense that non-exponential growth is…
We give a short proof of the strong law of large numbers based on duality for random walk
We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well…
We prove a strong law of large numbers for simultaneously testing parameters of a large number of dependent, Lancaster bivariate random variables with infinite supports, and discuss its implications.
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…
We consider the dynamics of a 1D system evolving according to a deterministic drift and randomly forced by two types of jumps processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
In this paper, we study random walks evolving on Z in a dynamic random environment that we assume to have time correlations that decrease polynomially fast. We show a law of large numbers by generalizing methods already used for the…
This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
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…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in…
We prove the law of large numbers and invariance principles for the tagged particle in the asymmetric exclusion process with long jumps when the process starts from its equilibrium measure.
We consider a random walk in a stationary ergodic environment in $\mathbb Z$, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right…
The point of view of the particle is an approach that has proven very powerful in the study of many models of random motions in random media. We provide a new use of this approach to prove the law of large numbers in the case of one or…
As the extension of uncorrelated single-valued random variables, set-valued case is studied in this paper. When the underlying space is of finite dimension, by using the support function, We shall prove the weak and strong laws of large…