Faster Random Walk Simulation ?!?

• To: mathgroup at smc.vnet.net
• Subject: [mg66177] Faster Random Walk Simulation ?!?
• From: "mfific at gmail.com" <mfific at gmail.com>
• Date: Wed, 3 May 2006 02:44:45 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear All,
I am running a simulation with Mathematica 5 that includes random walk
described below. The argument boundaryA is upper and lower boundary for
a random walk. Parameter "value" is just a constant arbitrarily set to
0.5. The output of the table function is the 10000 random walks, and
their path to either +5 or -5 boundary value.
While everything works as expected, it takes considerable duration of
time. For example it takes 2.6 seconds to generate the table output, on
a relatively fast computer.

I would very appreciate if any significantly faster solution could be
suggested.

value = .5

RandomWalk[boundaryA_] := Block[{l = {{0, 0}}, x = 0,
i = 0 }, While[boundaryA > x > -boundaryA,
x += If[Random[] > value, 1, -1];
l = Append[l, {++i, x}]];
l]

Timing[Table[RandomWalk[5], {i, 1, 10000}];]

Out[420]=
{2.672 Second, Null}

Thank you very much,

Mario Fific

Mario Fific
Cognitive Psychology, Cognitive Science
Indiana University
1101 E. 10th St.
Bloomington, IN  47405-7007

```

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