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A new technique for calculating the time-evolution, correlations and steady state spectra for nonlinear stochastic differential equations is presented. To illustrate the method, we consider examples involving cubic nonlinearities in an…

Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…

We introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. We focus on periodic boundary…

We analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time-periodic forces. We focus on the stochastic resonance and phase frequency synchronization of the collective variable,…

The dynamical properties of road traffic time series from North-Rhine Westphalian motorways are investigated. The article shows that road traffic dynamics is well described as a persistent stochastic process with two fixed points…

The emergence dynamics of traffic instability has always attracted particular attention. For several decades, researchers have studied the stability of traffic flow using deterministic traffic models, with less emphasis on the presence of…

We consider a system of non-interacting particles on a line with initial positions distributed uniformly with density $\rho$ on the negative half-line. We consider two different models: (i) each particle performs independent Brownian motion…

Stochastic resonance is a phenomenon in which fluctuations enhance an otherwise weak signal. It has been found in many different systems in paleoclimatology, biology, medicine, and physics. The classical stochastic resonance due to thermal…

We study Brownian particle motion in a double-well potential driven by an ac force. This system exhibits the phenomenon of stochastic resonance. Distribution of work done on the system over a drive period in the time asymptotic regime have…

Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…

Stochastic physics is a central pillar of modern research in many fields, but is rarely presented to undergrad students in a hands-on experiment. Here, we demonstrate how a human-scale, simple, and affordable experimental setup can be used…

Learning models or control policies from data has become a powerful tool to improve the performance of uncertain systems. While a strong focus has been placed on increasing the amount and quality of data to improve performance, data can…

We study analytically giant fluctuations and temporal intermittency in a stochastic one-dimensional model with diffusion and aggregation of masses in the bulk, along with influx of single particles and outflux of aggregates at the…

We consider lattice gas diffusive dynamics with creation-annihilation in the bulk and maintained out of equilibrium by two reservoirs at the boundaries. This stochastic particle system can be viewed as a toy model for granular gases where…

We consider overdamped diffusion processes driven out of thermal equilibrium and we analyze their dynamical steady fluctuations. We discuss the thermodynamic interpretation of the joint fluctuations of occupation times and currents; they…

Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid.…

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density…

Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation.…

Many recent works in control of electric power systems have investigated their synchronization through global performance metrics under external disturbances. The approach is motivated by fundamental changes in the operation of power grids,…