Related papers: Evolution of statistical averages: an interdiscipl…
A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a…
We study a generalized version of the Gross-Neveu model in 2+1 dimensions. The model is inspired from Graphene, which shows a linear dispersion relation near the Dirac points. The phase structure and the thermodynamic properties in the mean…
In this note, we give an overview of some results obtained in [3]. This latter work is devoted to the study of the one-dimensional nonlinear Schr{\"o}dinger equation with random initial conditions. Namely, we describe the nonlinear…
Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main…
Beliefs inform the behavior of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack…
Estimates of uncertainty or variance in experimental means are central to physics. This is especially the case for `world averages' of fundamental physical parameters in particle physics, which aggregate results from a number of experiments…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…
Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann-Gibbs standard…
Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution…
The superstatistics approach recently introduced by Beck [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism that aims to deal in a unifying way with a large variety of complex nonequilibrium systems, for which…
Bayesian linear inverse problems aim to recover an unknown signal from noisy observations, incorporating prior knowledge. This paper analyses a data-dependent method to choose the scale parameter of a Gaussian prior. The method we study…
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…
In this paper, we present a computational technique to deal with uncertainty in dynamic continuous models in Social Sciences. Considering data from surveys, the method consists of determining the probability distribution of the survey…