Related papers: Point estimates, Simpson's paradox and nonergodici…
Modern physics is founded on two mainstays: mathematical modelling and empirical verification. These two assumptions are prerequisite for the objectivity of scientific discourse. Here we show, however, that they are contradictory, leading…
Non-ergodicity impacts statistical inference in a diverse range of disciplines inside and outside of physics. However the concept of ergodicity is used inconsistently, and may refer to several nonequivalent notions. To help address this, we…
Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To…
One challenge in the estimation of financial market agent-based models (FABMs) is to infer reliable insights using numerical simulations validated by only a single observed time series. Ergodicity (besides stationarity) is a strong…
The theoretical cornerstone of statistical mechanics is the ergodic assumption that all accessible configurations of a physical system are equally likely. Here we show how such property arises when an open quantum system is continuously…
Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the…
The mathematical definitions of distinct concepts that are needed in building an ergodicity detection algorithm are introduced in a framework. This algorithmic framework is expressed in a discrete setting in an accessible manner for broader…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially…
Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
I prove a theorem on the precise connection of the time and phase space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively…
Although financial models violate ergodicity in general, observing the ergodic behavior in the markets is not rare. Policymakers and market participants control the market behavior in critical and emergency states, which leads to some…
This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system…
The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This…
We study conservative particle systems on W^S, where S is countable and W = {0, ..., N} or the natural numbers. The rate of a particle moving from site x to site y is given by p(x,y) b(eta_x, eta_y), where eta_z is the number of particles…
This paper studies maximisation of an average-cost-per-unit-time ergodic functional over impulse strategies controlling a Feller-Markov process. The uncontrolled process is assumed to be ergodic but, unlike the extant literature, the…
This paper introduces a novel approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from…
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…