Related papers: Properties of stationary cyclical processes
Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain…
We perform a qualitative analysis of the critical equation associated with a stationary ergodic Hamiltonian through a stochastic version of the metric method, where the notion of closed random stationary set, issued from stochastic…
We introduce a class of semiparametric time series models by assuming a quasi-likelihood approach driven by a latent factor process. More specifically, given the latent process, we only specify the conditional mean and variance of the time…
This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
We study the spectral properties of classical and quantum Markovian processes that are reset at random times to a specific configuration or state with a reset rate that is independent of the current state of the system. We demonstrate that…
Strong zero modes (SZMs) are conserved operators localised at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyse analogous operators in one-dimensional classical…
We investigate simple models for strictly non-ergodic stochastic processes $x_t$ ($t$ being the discrete time step) focusing on the expectation value $v$ and the standard deviation $\delta v$ of the empirical variance $v[x]$ of finite time…
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If…
The fraction r(t) of spins which have never flipped up to time t is studied within a linear diffusion approximation to phase ordering. Numerical simulations show that, even in this simple context, r(t) decays with time like a power-law with…
Periodically-driven open quantum systems that never thermalize exhibit a discrete time-crystal behavior, a non-equilibrium quantum phenomenon that has shown promise in quantum information processing applications. Measurements of…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
We consider stochastic processes $Y(t)$ which can be represented as $Y(t)=(X(t))^s, s \in \mathbb{N},$ where $X(t)$ is a stationary strictly sub-Gaussian process and build a wavelet-based model that simulates $Y(t)$ with given accuracy and…
We re-analyze the quasi-linear self consistent dynamics for the beam-plasma instability, by comparing the theory predictions to numerical simulations of the corresponding Hamiltonian system. While the diffusive features of the asymptotic…
In this work we introduce a class of dynamic models for time series taking values on the unit interval. The proposed model follows a generalized linear model approach where the random component, conditioned on the past information, follows…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
In this work we study a nonlinear Volterra equation with non-symmetric feedback that arises as a particular case of the Gurtin-MacCamy model in population dynamics. We are particularly interested in the existence of slowly oscillating…
We propose strongly consistent estimators of the $\ell_1$ norm of the sequence of $\alpha$-mixing (respectively $\beta$-mixing) coefficients of a stationary ergodic process. We further provide strongly consistent estimators of individual…
This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger…