3-D Wiener process

Hermann.Singer@FernUni-Hagen.de

Wiener//Unprotect;
Wiener[y0_,dt_,T_]:=
Module[{p,y},
p=y0//Length;
y=RandomReal[NormalDistribution[0,dt],{T,p}];
FoldList[Plus,y0,y]
]

Clear[seed,T,M];

Manipulate[

y0=Array[0.&,dd=3];
g=Table[
SeedRandom[seed*n//Ceiling];
w=Wiener[y0,10^-3,T//Ceiling];
ListPointPlot3D[w,AspectRatio->1,PlotRange->.2{{-1,1},{-1,1},{-1,1}},
		     DisplayFunction->Identity,PlotStyle->Directive[Hue[n/M],PointSize[.001]]],

{n,1,M}];

Show[g,ImageSize->600]

,{seed,1,100,1},{{M,3,"trajectories"},1,20,1},{{T,5000,"timepoints"},2,10000},SaveDefinitions->True]