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We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…

Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future…

We extend deterministic port-Hamiltonian systems (PHS) to a stochastic framework by means of stochastic differential equations. As the dissipation inequality plays a crucial role for deterministic PHS, we develop several passivity concepts…

Given an unknown dynamic system such as a coupled harmonic oscillator with $n$ springs and point masses. We are often interested in gaining insights into its physical parameters, i.e. stiffnesses and masses, by observing trajectories of…

The article considers the problem of identifying the variable frequency of a sinusoidal signal. To obtain a regression model of the signal, an iterative differentiation of the original analytical expression is performed, and the swapping…

The asteroseismic analysis of stellar power density spectra is often computationally expensive. The models used in the analysis may use several dozen parameters to accurately describe features in the spectra caused by oscillation modes and…

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

We introduce the problem of estimation of the parameters of a dynamically selected population in an infinite sequence of random variables and provide its application in the statistical inference based on record values from a non-stationary…

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…

Speech enhancement in hearing aids remains a difficult task in nonstationary acoustic environments, mainly because current signal processing algorithms rely on fixed, manually tuned parameters that cannot adapt in situ to different users or…

We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed…

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…

The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…

Standard system identification methods often provide inconsistent estimates with closed-loop data. With the prediction error method (PEM), this issue is solved by using a noise model that is flexible enough to capture the noise spectrum.…

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…

In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…

Gaussian functions are commonly used in different fields, many real signals can be modeled into such form. Research aiming to obtain a precise fitting result for these functions is very meaningful. This manuscript intends to introduce a new…

This article discusses aeroacoustic imaging methods based on correlation measurements in the frequency domain. Standard methods in this field assume that the estimated correlation matrix is superimposed with additive white noise. In this…