[Numpy-discussion] Valid algorithm for generating a 3D Wiener Process?
Daπid
davidmenhur at gmail.com
Fri Sep 27 04:00:53 EDT 2013
On 26 September 2013 10:02, Daπid <davidmenhur at gmail.com> wrote:
> The simplest way is to do it in cartesian coordinates: take x, y, and z
> independently from N(0,1). If you want to generate only one normal number
> per step, consider the jacobian in the angles.
Actually, this is wrong, as it would allow displacements (at 1 sigma) of 1
along the axis, but up to sqrt(3) along diagonals. What you actually want
is a multivariate normal distribution with covariance proportional to the
identity (uncorrelation between axis and isotropy).
See formulae here:
http://en.wikipedia.org/wiki/Multivariate_normal_distribution
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