随机过程matlab程序

% PPT 例2 一维正态密度与二维正态密度

syms x y;

s=1; t=2;

mu1=0; mu2=0; sigma1=sqrt((1+s^2)); sigma2=sqrt((1+t^2));

x=-6:0.1:6;

f1=1/sqrt(2*pi*sigma1)*exp(-(x-mu1).^2/(2*sigma1^2));

f2=1/sqrt(2*pi*sigma2)*exp(-(x-mu2).^2/(2*sigma2^2));

plot(x,f1,'r-',x,f2,'k-.')

rho=(1+s*t)/(sigma1*sigma2);

f=1/(2*pi*sigma1*sigma2*sqrt(1-rho^2))*exp(-1/(2*(1-rho^2))*((x-mu1)^2/sigma1^2-2*rho*(x-mu1)*(y-mu2)/(sigma1*sigma2)+(y-mu2)^2/sigma2^2));

ezsurf(f)

-6-4-20246

x 44798133900177/281474976710656 exp(-5/2 x 2+3 x y-y 2)

y

% % The daily log returns on the stock have a mean of 0.05/year and a standard deviation of 0.23/year. These can be converted to rates per trading day by deviding by 253 and sqrt(253), respectively.

Question 1: What is the probability that the value of the stock will be below $950,000 at the close day of at least one of the next 45 trading days?

clear;

niter=1.0E5; % number of iterations

below=repmat(0,1,niter); % set up storage

randn('seed',0);

for i=1:niter

r=normrnd(0.05/253,0.23/sqrt(253),1,45); % generate random numbers

logPrice=log(1.0E6)+cumsum(r);

minlogP=min(logPrice); % minmum price over next 45 days

below(i)=sum(minlogP

end

Pro=mean(below)

% P29 随机相位正弦波仿真

% 1 time simulation

w=2; N=1000; mu=2; sigma=3;

s=rand('state');

A=mu+sigma*randn(1,N); % A=normrnd(mu,sigma,1,N)

theta=-pi+2*pi*rand(1,N);

t=1:N;

x=A.*cos(w*t+theta);

capmu=mean(x)

tao=1

x1=A.*cos(w*(t+tao)+theta);

capgamma=mean((x-capmu).*(x1-capmu))

% m time simulation

clear;

w=2; N=1000; mu=2; sigma=3;

m=500;capmu1=[];capgamma1=[];

for i=1:m

s=rand('state');

A=mu+sigma*randn(1,N);

theta=-pi+2*pi*rand(1,N);

t=1:N;

x=A.*cos(w*t+theta);

capmu=mean(x);

capmu1=[capmu1,capmu];

tao=1;

x1=A.*cos(w*(t+tao)+theta); capgamma=mean((x-capmu).*(x1-capmu)); capgamma1=[capgamma1,capgamma];

end

plot(1:m,capmu1,'*',1:m,capgamma1,'o')

capmu=mean(capmu1);

capgamma=mean(capgamma1);

err1=mean((capmu1-0).^2);

gamma=(sigma^2+mu^2)*cos(w*tao)/2;

err2=mean((capgamma1-gamma).^2); [capmu,capgamma; err1, err2]

% 输出：

0.0058 -2.7005

0.0065 0.0736