function intdwdw
% Fig. 2.1 Example MATLAB code for integral of (dW)^2 (3/2007):
clc % clear variables;
t0 = 0.0; tf = 1.0; 
n = 1.0e+4; nf = n + 1; % set time grid: (n+1) subintervals
dt = (tf-t0)/nf;  %       and (n+2) points; 
% replace these particular values according the application; 
sqrtdt = sqrt(dt); % dW(i) noise time scale so E[dW] = 0;
kstate = 1; randn('state',kstate); % Set randn state
%    for repeatability;
dW = sqrtdt*randn(nf,1); % simulate (n+1)-dW(i)'s sample;
t = t0:dt:tf; % get time vector t;
W = zeros(1,nf+1); % set initial diffusion noise condition;
sumdw2 = zeros(1,nf+1); % set initial integral sum;
for i = 1:nf % simulate integral sample path.
    W(i+1) = W(i) + dW(i); % sum diffusion noise;
    sumdw2(i+1) = sumdw2(i) + (dW(i))^2; % sum whole integrand;
end
fprintf('\n\nFigure 1: int[(dW)^2](t) versus t\n');
nfig = 1;
figure(nfig);
scrsize = get(0,'ScreenSize'); % figure spacing for target screen
ss = [5.0,4.0,3.5]; % figure spacing factors
plot(t,sumdw2,'k-',t,t,'k--','LineWidth',2); % plot sum and t;
title('\int(dW)^2(t) Simulations versus t'...
    ,'FontWeight','Bold','Fontsize',44);
ylabel('\int(dW)^2(t) and t, States'...
    ,'FontWeight','Bold','Fontsize',44);
xlabel('t, Time'...
    ,'FontWeight','Bold','Fontsize',44);
hlegend=legend('\int(dW)^2(t)','t'...
    ,'Location','Southeast');
set(hlegend,'Fontsize',36,'FontWeight','Bold');
set(gca,'Fontsize',36,'FontWeight','Bold','linewidth',3);
set(gcf,'Color','White','Position' ...
   ,[scrsize(3)/ss(nfig) 60 scrsize(3)*0.60 scrsize(4)*0.80]); %[l,b,w,h]
% End Code