Stochastic numerical methods

Numerical Methods for Second-order Stochastic Equations

We seek numerical methods for second-order stochastic differential equations that accurately reproduce the stationary distribution for all values of damping. A complete analysis is possible for linear second-order equations (damped harmonic oscillators with noise), where the statistics are Gaussian and can be calculated exactly in the continuous-time and discrete-time cases. A matrix equation i...

Numerical Solution Methods in Stochastic Chemical Kinetics

Numerical Methods for Stochastic Differential Equations

Approximately a quarter century ago, very early in my career when I was publishing rather theoretical results about stochastic differential equations, I received a letter (this predates e-mail) from a fellow researcher who had seen my work and was asking if I had an algorithm suitable for implementing my ideas on a computing machine. Not only did I not have such an algorithm, the idea had not o...

Numerical Methods for Stochastic Differential Equations

Stochastic differential equations (SDE's) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes for solving stochastic equations is outlined here. High-order numerical methods are developed for the integration of stochastic differential equations with st...

Numerical Methods for Stochastic Differential Games