相关论文: On Large Deviation Property of Recurrence Times
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
We give a criterion to determine the large deviation rate functions for abstract dynamical systems on towers. As an application of this criterion we show the level 2 large deviation principle for some class of smooth interval maps with…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large $n$, a networked data…
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…
We prove that multimodal maps with an absolutely continuous invariant measure have exponential return time statistics around a.e. point. We also show a `polynomial Gibbs property' for these systems, and that the convergence to the entropy…
We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…
Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…
Given an R^d-valued supercritical branching Wiener process, let D(A,T) be the number of particles in a subset A of R^d at time T, (T=0,1,2,...). We provide a complete asymptotic expansion of D(A,T) as T goes to infinity, generalizing the…
The meaning of thermodynamic descriptions is found in large-deviations scaling of the fluctuations probabilities. The primary large-deviations rate function is the entropy, which is the basis for both fluctuation theorems and for…
These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
We show in this note that the asymptotic spectral distribution, location and distribution of the largest eigenvalue of a large class of random density matrices coincide with that of Wishart-type random matrices using proper scaling. As an…
This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…
To investigate the complex dynamics of a biological neuron that is subject to small random perturbations we can use stochastic neuron models. While many techniques have already been developed to study properties of such models, especially…
We consider the quasi-deterministic behavior of systems with a large number, $n$, of deterministically interacting constituents. This work extends the results of a previous paper [J. Stat. Phys. 99:1225-1249 (2000)] to include vector-valued…
In the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
The asymptotic behavior for entropy numbers of general Fourier multiplier operators of multiple series with respect to an abstract complete orthonormal system $\{\phi_{\textbf{m}}\}_{\textbf{m}\in \mathbb{N}^d_0}$ on a probability space and…
This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature…