Exact numerical simulation of the OrnsteinUhlenbeck process and its integral
Abstract
A numerical simulation algorithm that is exact for any time step ∆t>0 is derived for the OrnsteinUhlenbeck 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 RL circuit, provided appropriate values are assigned to the OrnsteinUhlenbeck relaxation time τ and diffusion constant c. A simple Taylor expansion in ∆t of the exact simulation formulas shows how the firstorder 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 zeroτ limit theorem.
 Publication:

Physical Review E
 Pub Date:
 August 1996
 DOI:
 10.1103/PhysRevE.54.2084
 Bibcode:
 1996PhRvE..54.2084G
 Keywords:

 02.70.Lq;
 02.50.Ga;
 02.60.Cb;
 05.40.+j;
 Markov processes;
 Numerical simulation;
 solution of equations