Related papers: Stochastic Time-Series Spectroscopy
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
The problem of estimating parameters of a deterministic jump or piecewise linear model is considered. A subspace technique referred to as spectral clustering on subspace (SCS) algorithm is proposed to estimate a set of linear model…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
We propose a new statistical test to identify non-stationary frequency-modulated stochastic processes from time series data. Our method uses the instantaneous phase as a discriminatory statistics with reliable critical values derived from…
Spin Noise Spectroscopy (SNS) is an experimental approach to obtain correlators of mesoscopic spin fluctuations in time by purely optical means. We explore the information that this technique can provide when it is applied to a weakly…
We propose solution of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of a continuous time stochastic process with periodically correlated increments based on observations of…
Spectrum sensing is essential in cognitive radio to enable dynamic spectrum access. In many scenarios, primary user signal must be detected reliably in low signal-to-noise ratio (SNR) regime under required sensing time. We propose to use…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method…
Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…
Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
Nonlinear stochastic differential equations provide one of the mathematical models yielding 1/f noise. However, the drawback of a single equation as a source of 1/f noise is the necessity of power-law steady-state probability density of the…
Raman spectroscopy uses light scattering to extract information on low-energy excitations of solids. The Raman process is described by diagrams which are fourth order in the light-matter interaction, and in particular the resonant…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
A two-state system (TSS) under time-periodic perturbations (to be regarded as input signals) is studied in connection with self-tuning (ST) of threshold and stochastic resonance (SR). By ST, we observe the improvement of signal-to-noise…