RandomWalk[n_, d_] := NestList[(# + Table[Random[Real, {-1, 1}], {d}]) &, Table[0, {d}], n];
ThreeDim = RandomWalk[5000, 3];ThreeDim = RandomWalk[5000, 3];
I defined a security boundary for a random walk:
p = 5000;(*steps*)
tc = 15;(*cube edge length*)
tp = 0.2;
random = Accumulate[
Join[{RandomReal[{-tc, tc}/2, 3]},
RandomVariate[NormalDistribution[0, tp], {p, 3}]]];
periodizedWalk = Mod[random, tc, -tc/2];
splitPeriodizedWalk =
Split[periodizedWalk, EuclideanDistance[#1, #2] < tc/2 &];
With[{cube = First[PolyhedronData["Cube"]]},
Graphics3D[{{Opacity[0.1], Scale[cube, tc]}, Line[random]},
Boxed -> False]]
and now i want to obtain a sample of the random times at which the random walk crosses the boundary for the first time. Something like this:
W = {}; For[i = 1, i <= 5000, i++,
PosFinal = {0, 0}; EME = 1;
While[True,
PosFinal = PosFinal + step[Random[]];
If[Norm[PosFinal] > 15, Break[]];
EME=EME+1;
];
W=Append[W,EME];
]
but i want these two codes to be related and the second one that gives me the sample of the random times at which the random walk crosses the boundary for the first time is very slow, my pc takes too much time to run it. Would like some help please 
