Numerical Integration of Langevin Equation

dsdsuster · Jan 20, 2014

Can anyone explain to me why the gaussian white noise term is multiplied by the square root of the time differential when we turn the Langevin differential equation into a finite difference equation for the purposes of integration?

http://pre.aps.org/pdf/PRE/v50/i6/p4404_1

The step I don't understand is the change in the last term in going from equation 3 to 4.

Any help would be greatly appreciated, thanks!

mathman · Jan 21, 2014

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dsdsuster · Jan 22, 2014

equation 3:

equation 4:

Discrete-time stochastic update equation: rho(i,t+Δt) − rho(i,t) = [a rho(i,t) − b rho(i,t)² + D ∇̃² rho(i,t)] Δt + sqrt(rho(i,t) Δt) Y(i,t), with the square-root term on a second line.

Here are the two equations. Thanks for your help!

Numerical Integration of Langevin Equation

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