Re: Weiner process
- To: mathgroup at smc.vnet.net
- Subject: [mg63931] Re: Weiner process
- From: Roger Bagula <rlbagulatftn at yahoo.com>
- Date: Mon, 23 Jan 2006 04:11:47 -0500 (EST)
- References: <dqqc98$m0j$1@smc.vnet.net> <dqt15s$jlj$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
The good and fast Lorenz plot.
Do you have some references on this method?
Or did you invent it.
I've never seen it before.
Steve Luttrell wrote:
> A simple way to generate a random walk is as follows:
>
> x[t_] := x[t] = x[t - 1] + Random[Real, {-0.01, 0.01}];
> x[t_] := 0 /; t <= 0;
>
> This is defined as a "finite state machine", whose initial state is 0. It
> uses a uniformly distributed step size, and it "memorises" each step as it
> is generated. This approach generalises readily.
>
> Plot the first 1000 steps of the random walk:
>
> ListPlot[Table[x[t], {t, 0, 1000}], PlotJoined -> True];
>
> For your entertainment here is the Lorenz attractor done in the same style
> as above:
>
> Needs["Graphics`Graphics3D`"];
>
> e = 0.013;
> r = 28;
>
> x[t_] := x[t] = {x[t - 1][[1]] + 10*e*(x[t - 1][[2]] - x[t - 1][[1]]),
> x[t - 1][[2]] + e*(r*x[t - 1][[1]] - x[t - 1][[1]]*x[t - 1][[3]] -
> x[t - 1][[2]]), x[t - 1][[3]] + e*(x[t - 1][[1]]*x[t - 1][[2]] -
> (8*x[t - 1][[3]])/3)};
> x[1] = {0.1, 0.1, 10.};
>
> ScatterPlot3D[Table[x[t], {t, 1000}], PlotJoined -> True, AspectRatio -> 1];
>
> Steve Luttrell
>
> "Don" <ddarling at math.uci.edu> wrote in message
> news:dqqc98$m0j$1 at smc.vnet.net...
>
>>For a Monte Carlo simulation I need samples of the Brownian motion
>>(Wiener)process X(t), 0<t<1. Does anyone know of a data base where I can
>>find them, or of a program to generate them?
>>
>>
>
>
>