Numerical Integration of Langevin Equation

[dsdsuster]

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]

Can't access - requires membership.

 

[dsdsuster]

equation 3:

equation 4:

Here are the two equations. Thanks for your help!