1996/08/01 by Daniel T. Gillespie · 5 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Brownian motion #Charge (physics) #Computer science #Constant (computer programming) #Exact solutions in general relativity #Langevin equation #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Order (exchange) #Ornstein–Uhlenbeck process #Physics #Position (finance) #Quantum mechanics #Relaxation (psychology) #Simple (philosophy) #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #Stochastic process #stochastic dynamics and bifurcation
paper · doi:10.1103/physreve.54.2084
openalex publication_date 1996/08/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/03
A numerical simulation algorithm that is exact for any time step \ensuremathΔt>0 is derived for the Ornstein-Uhlenbeck process X(t) and its time integral Y(t). The algorithm allows one to make efficient, unapproximated simulations of, for instance, the velocity and position components of a particle undergoing Brownian motion, and the electric current and transported charge in a simple R-L circuit, provided appropriate values are assigned to the Ornstein-Uhlenbeck relaxation time \ensuremathτ and diffusion constant c. A simple Taylor expansion in \ensuremathΔt of the exact simulation formulas shows how the first-order simulation formulas, which are implicit in the Langevin equation for X(t) and the defining equation for Y(t), are modified in second order. The exact simulation algorithm is used here to illustrate the zero-\ensuremathτ limit theorem. \textcopyright 1996 The American Physical Society.