Topological classification of Brownian orbits
Topological classification of Brownian orbits is a scholarly work by Fumihiko Tanaka, published in 2012 in ''Journal of Chemical Physics''. The main subjects of the publication include mathematics, Stochastic resonance, mathematical analysis, homotopy, diffusion process, stochastic thermodynamics, constant, position, Brownian motion, Brownian excursion, limit, and orbit. This paper presents the exact formula for the bivariate probability distribution function of a Brownian particle as a function of its position and velocity, whose orbit makes a specified number of turns around an infinite straight line.