Related papers: Time vs. Ensemble Averages for Nonstationary Time …
Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random…
In this paper, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling…
Various nonparametric approaches for Bayesian spectral density estimation of stationary time series have been suggested in the literature, mostly based on the Whittle likelihood approximation. A generalization of this approximation has been…
We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the…
A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random $N\times N$ matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and…
While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittle's Likelihood, involving the second order…
We study the limiting behavior of multiple ergodic averages involving several not necessarily commuting measure preserving transformations. We work on two types of averages, one that uses iterates along combinatorial parallelepipeds, and…
We consider ensemble averaged theories with discrete random variables. We propose a suitable measure to do the ensemble average. We also provide a mathematical description of such ensemble averages of theories in terms of Poisson point…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments…
In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…
In this paper, we formulate and investigate a generalized consensus algorithm which makes an attempt to unify distributed averaging and maximizing algorithms considered in the literature. Each node iteratively updates its state as a…
This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of…
This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral…
In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while…
For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…
Previous approaches to modelling interval-censored data have often relied on assumptions of homogeneity in the sense that the censoring mechanism, the underlying distribution of occurrence times, or both, are assumed to be time-invariant.…
We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present exact analytical results for the…