http://www.mapleprimes.com/posts/42391-Simulation-Of-Brownian-Motion en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 16 Jun 2026 15:18:55 GMT Tue, 16 Jun 2026 15:18:55 GMT The latest comments added to the Post, Simulation of Brownian Motion http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/42391-Simulation-Of-Brownian-Motion http://www.mapleprimes.com/posts/42391-Simulation-Of-Brownian-Motion?ref=Feed:MaplePrimes:Simulation of Brownian Motion:Comments#comment79307 <pre> Nice stuff, Alec :-) Especially I like your construct for W ... The size comes through the plot. How about exporting or saving? </pre> The latest comments added to the Post, Simulation of Brownian Motion 79307 Sun, 22 Oct 2006 21:28:01 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/posts/42391-Simulation-Of-Brownian-Motion?ref=Feed:MaplePrimes:Simulation of Brownian Motion:Comments#comment86288 Axel, Thank you. Exporting to gif worked out OK (except cutting off the labels on the y-axis) - that's how I got the pictures, I didn't do any editing of them later. Saving took some time (a few minutes), but seemed OK, too. Perhaps, if I waited longer, the saved file could be opened. I tried to open it only once and waited only for about 3 minutes. Later I thought that I could just export all plots to gifs, remove output, and insert pictures from the exported gifs after that. That should make the worksheet considerably smaller. Alec The latest comments added to the Post, Simulation of Brownian Motion 86288 Sun, 22 Oct 2006 23:32:54 Z alec alec http://www.mapleprimes.com/posts/42391-Simulation-Of-Brownian-Motion?ref=Feed:MaplePrimes:Simulation of Brownian Motion:Comments#comment86287 <pre> BM := proc(n::posint, m::posint) local X; uses Statistics,ListTools; X := RandomVariable(Normal(0,1/sqrt(n))); '&lt;0,PartialSums([seq(i,i=Sample(X,n))])[]&gt;'$m; end proc: BM2 := proc(n::posint, m::posint) local A, i; A := ArrayTools:-Alias(Statistics:-Sample(Normal(0, 1/sqrt(n)), m*n), [1..m, 1..n]); for i to m do A[i] := Statistics:-CumulativeSum(A[i]); end do; A; end proc; > time(BM(200, 200)); 0.924 > time(BM2(200, 200)); 0.048 > time(BM2(1000, 1000)); 0.956 </pre> -Alex The latest comments added to the Post, Simulation of Brownian Motion 86287 Sun, 22 Oct 2006 23:59:33 Z alex alex http://www.mapleprimes.com/posts/42391-Simulation-Of-Brownian-Motion?ref=Feed:MaplePrimes:Simulation of Brownian Motion:Comments#comment90883 Alex, Thank you. I waited for that. I thought that there should be an effective way of doing that with vectors, without converting them to lists, but couldn't find it. Alec The latest comments added to the Post, Simulation of Brownian Motion 90883 Mon, 23 Oct 2006 00:15:41 Z Alec Mihailovs Alec Mihailovs http://www.mapleprimes.com/posts/42391-Simulation-Of-Brownian-Motion?ref=Feed:MaplePrimes:Simulation of Brownian Motion:Comments#comment79305 <pre> BM3 := proc(n::posint, m::posint) local A, i, CS; A := ArrayTools:-Alias(Statistics:-Sample(Normal(0, 1/sqrt(n)), m*n), [1..m, 1..n]); CS:=proc(L,n) local LL, s; LL:=hfarray(1..n); s:=0; for i from 1 to n do s:= s + L[i]; LL[i]:=s; end do; LL; end proc; #st:=time(): for i to m do A[i] :=CS(A[i],n); end do; #print( time()-st); A; #print( A[1]); end proc: gc(): time(tmp=BM1(200, 200)); gc(): time(tmp=BM2(200, 200)); gc(): time(tmp=BM3(200, 200)); 4.519 0.189 0.019 gc(): time(tmp=BM2(1000, 1000)); gc(): time(tmp=BM3(1000, 1000)); 1.780 0.334 PS: may be one should clean the sheet, otherwise the (large) arrays are stored with it. </pre> The latest comments added to the Post, Simulation of Brownian Motion 79305 Mon, 23 Oct 2006 02:32:03 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/posts/42391-Simulation-Of-Brownian-Motion?ref=Feed:MaplePrimes:Simulation of Brownian Motion:Comments#comment86285 Axel, Excellent idea! Thank you! I'll try to incorporate it and maybe we could submit the worksheet to the Maple Application center, with 4 authors: you, Alex, Stephen Ryder, and me. _________ Alec Mihailovs <a href="http://mihailovs.com/Alec/">http://mihailovs.com/Alec/</a> The latest comments added to the Post, Simulation of Brownian Motion 86285 Mon, 23 Oct 2006 05:00:23 Z alec alec