Related papers: Stochastic Dynamics of Time Correlations in Comple…

This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for…

Sensitivity analysis is a process of computing sensitivity indices, which are certain measures of importance of parameters in influencing the outputs of mathematical models. Sensitivity indices computed in variance-based sensitivity…

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…

This paper is concerned with a data-driven technique for constructing finite Markov decision processes (MDPs) as finite abstractions of discrete-time stochastic control systems with unknown dynamics while providing formal closeness…

Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems…

Recurrence entropy $(\cal S)$ is a novel time series complexity quantifier based on recurrence microstates. Here we show that $\mathsf{max}(\cal S)$ is a \textit{parameter-free} quantifier of time correlation of stochastic and chaotic…

Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical…

We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by "controlled" Markov noise. In particular, the faster and slower recursions have non-additive controlled Markov noise…

For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…

We present a study of the equilibration process of nonequilibrium systems by means of molecular dynamics simulation technique. The nonequilibrium conditions are achieved in systems by defining velocity components of the constituent atoms…

We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…

Stochastic thermodynamics investigates energetic and entropic bounds in small systems. Foundational results, e.g., the first and second laws, predominantly rely on the Markov (memoryless) assumption. Although physicists recognise that the…

Stochastic resetting describes dynamics which are reinitialized to a reference state at random times. These protocols are attracting significant interest: they can stabilize nonequilibrium stationary states, generate correlations in…

The introduced entropy functional's (EF) information measure of random process integrates multiple information contributions along the process trajectories, evaluating both the states' and between states' bound information connections. This…

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…

A surrogate data analysis is presented, which is based on the fluctuations of the ``entropy'' $S$ defined in the natural time-domain [Phys. Rev. E {\bf 68}, 031106, 2003]. This entropy is not a static one as, for example, the Shannon…

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…

In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…

We study the non-Markovian random continuous processes described by the Mori-Zwanzig equation. As a starting point, we use the Markovian Gaussian Ornstein-Uhlenbeck process and introduce an integral memory term depending on the past of the…