Geometric Brownian motion

Statistics

Fractional Brownian motion

Brownian motion

Physics

Statistical physics

Engineering

Aerospace engineering

Spectral density

Pure mathematics

Range (aeronautics)

Innovation diffusion

Mathematics

Computer science

Knowledge management

Quantum mechanics

Diffusion process

Diffusion

Stochastic process

Field (mathematics)

Journal of Statistical Mechanics Theory and Experiment

Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in general have been addressed in Statistical Physics. In particular, there now exists a very large range of applications of stochastic processes in various disciplines. Here we provide a summary of some of the recent developments in the field of stochastic processes, highlighting both the experimental findings and theoretical frameworks.

Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion