In this paper a new operational definition of Rényi divergence and Rényi entropy is presented. Other operational definitions are mentioned.

Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such...

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 nontrivial stationary state. We discuss the results and...

We study the effect of a field on the span of a particle diffusing on a line, i.e., the length covered by a Brownian particle which moves on a line for time t in the presence of a constant field. This is the one-dimensional analog of the Wiener sausage volume. Exact expressions are found for the...

High-frequency returns of the DAX German blue chip stock index are used to test geometric Brownian motion, the standard model for financial time series. Even on a 15-s time scale, the linear correlations of DAX returns have a zero-time delta function which carries 90% of the weight, while the...

The Kramers’ equation of Brownian motion is applied to investigate the motion of a colloidal particle in a medium subjected to a temperature gradient. The equation is generalized in two ways. First, a chemical force is included in order to account for the non-ideality of the colloidal...

We develop a simple numerical model for an asymmetrically polymerizing actin filament. The model is compared to the flashing ratchet and its velocity and efficiency are calculated exactly. The ratchet nature of such a filament is explained and a quantity called mean jump moment is introduced to...

We model a tiny heat engine as a Brownian particle that moves in a viscous medium in a sawtooth potential (with or without load) assisted by alternately placed hot and cold heat baths along its path. We find closed form expression for the steady-state current as a function of the model...

Brownian motion in a confined geometry has been studied using both light scattering and digital video microscopy. The particles were trapped between two nearly parallel walls making their confinement position dependent. Consequently, not only did we measure a diffusion coefficient which depended...

The long-time rotational motion of a set of rigid bodies immersed in a viscous fluid is studied on the basis of the linearized Navier–Stokes equations. After an initial twist applied to one of the bodies the rotational motion of each of them decays at long times with a t-5/2 long-time tail....