Related papers: Comments on arXiv:1811.00154 [astro-ph.IM] "AGN Va…

We present a study of variability time scales in a large sample of Active Galactic Nuclei at several frequencies between 4.8 and 230 GHz. We investigate the differences of various AGN types and frequencies and correlate the measured time…

Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

The damped random walk (DRW) process is one of the most commonly used and simplest stochastic models to describe variability of active galactic nuclei (AGN). An AGN light curve can be converted to just two DRW model parameters - the signal…

Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…

Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…

A simple, model-independent method to quantify the stochastic variability of active galactic nuclei (AGNs) is the structure function (SF) analysis. If the SF for the timescales shorter than the decorrelation timescale $\tau$ is a single…

The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades…

Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and…

We study backward stochastic differential equations (BSDEs) for time-changed L\'evy noises when the time-change is independent of the L\'evy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for…

Understanding how a system loses memory of its initial state is a central problem in probability and statistics. In this manuscript, we introduce the notion of abrupt decorrelation, which explicitly characterises a sharp and sudden loss of…

GRS 1915+105 is a prominent black hole system exhibiting variability over a wide range of time scales and its observed light curves have been classified into 12 temporal states. Here we undertake a complete analysis of these light curves…

MHD Turbulence is a critical component of the current paradigms of star formation, particle transport, magnetic reconnection and evolution of the ISM. Progress on this difficult subject is made via numerical simulations and observational…

Anomaly detection is the task of detecting data which differs from the normal behaviour of a system in a given context. In order to approach this problem, data-driven models can be learned to predict current or future observations.…

Determining whether the flux distribution of an Astrophysical source is a Gaussian or a log-normal, provides key insight into the nature of its variability. For lightcurves of moderate length ($< 10^3$), a useful first analysis is to test…

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully…

In this paper, we introduce a class of linear time-varying dynamic-algebraic equations(LTVDAE) of tractability index one on arbitrary time scales. We propose a procedure for the decoupling of the considered class LTVDAE. A projector…

We consider a setting, where the output of a linear dynamical system (LDS) is, with an unknown but fixed probability, replaced by noise. There, we present a robust method for the prediction of the outputs of the LDS and identification of…

In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…