matlab arr3(5:end),随机过程matlab程序

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1、基本操作-5/(4.8+5.32)八2 area=pi \*2.5八2 x1=1+1/2+1/3+1/4+1/5+1/6 exp(acos(0.3) a=1 2 3;4 5 6;7 8 9 a=1:3,4:6,7:9a1=6: -1:1a=eye(4) a1=eye(2,3)b=zeros(2,10) c=ones(2,10) c1=8\*ones(3,5)d=zeros(3,2,2) ；r1=rand(2, 3) r2=5-10\*rand(2, 3) r4=2\*randn(2,3)+3 arr1=1.1 -2.2 3.3 -4.4 5.5 arr1(3) arr1(1 4) arr1(1:2:5。

2、) arr2=1 2 3; -2 -3 -4;3 4 5 arr2(1,:) arr2(:,1:2:3) arr3=1 2 3 4 5 6 7 8 arr3(5:end) arr3(end)绘图x=0:1:10;y=x.A2-10\*x+15;plot(x,y)x=0:pi/20:2\*pi y1=sin(x);y2=cos(x);plot(x,y1,b-);hold on; plot(x,y2, -)k; legend ( sin xcos x );x=0:pi/20:2\*pi;y=sin(x); figure(1) plot(x,y, r-) grid on以二元函数图z = xexp(-xA。

3、2-yA2)为例讲解基本操作，首先需要利用meshgrid函数生成 X-Y 平面的网格数据，如下所示：xa = -2:0.2:2;ya = xa;x,y = meshgrid(xa,ya);z = x.\*ex p(-x.A2 - y.A2);mesh(x,y,z);建立 M 文件function fenshu( grade ) if grade 95.0disp( The grade is A. else);if grade 86.0disp( The grade is B. else);The grade is C.);if grade 76.0 disp(elseifdisp(elsegr。

4、ade 66.0The grade is D.);disp(The grade is F.);endendendend end function y=func(x) if abs(x)=t1(i) & tt1(m)N=N,m;endendplot(0:0.1:(t1(m)+1),N,r-)%输出:09080706050403020100102030405060708090100% P48非齐次泊松过程仿真% simulate 10 times clear;% exprn d(lamda.seed,1 ); set seedsm=10; lamda=1; x=; for i=1:ms=rand(。

5、 seed); x=x,ex prn d(lamda); t仁cumsum(x);end x,t1N=; T=;for t=0:0.1:(t1(m)+1)T=T,t.A3;% time is adjusted, cumulative inten sity fun cti on is t3.if t=t1(i) & tt1(m)N=N,m;endend plot(T,N, r-) % out put ans =0.42200.42203.33233.75430.16353.91780.06833.98610.38754.37360.27744.65100.29694.94790.93595.88。

6、380.42246.30621.76508.0712109876543218006007000100200300400500010 times simulati on10090807060504030201024x 10506 8 10100 times simulatio n2% P50复合泊松过程仿真 % simulate 100 times clear;niter=100;lamda=1;% iterate n umber % arrivi ng rate,s)t=inp ut( Input a time:for i=1: ni terrand( state,sum(clock);x=e。

7、x prn d(lamda);t1=x;% in terval timewhile t1=t1(i) & tt1(m)X=X,t2(m);endendplot(0:0.1:(t1(m)+1),X,r-)跳跃度服从0,1均匀分布情形跳跃度服从(1, 1/2)分布情形201510500102030405060708090-550Lr45J.45940-40-35-35-30302525E20-20-1-15-15-10105-5-00020406080100120020406080100120跳跃度服从t( 10)分布情形% Simulate the probability that sales 。

8、revenue falls in some interval. (e.g. example 3.3.6 in teaching material) clear;niter=1.0E4; lamda=6;t=720; above=repmat(0,1,niter);% number of iterations% arriving rate (unit:minute) % 12 hours=720 minutes% set up storagefor i=1:niterrand( state,sum(clock) x=exprnd(lamda); n=1;while x=t% arriving t。

9、imen=n;elsen=n+1;endendz=binornd(200,0.5,1,n);y=sum(z);above(i)=sum(y432000); end% generate n salespro=mean(above)Output: pro =0.3192% Simulate the loss pro. For a Compound Poisson process clear;niter=1.0E3; lamda=1; t=input(Input a time:,s) below=repmat(0,1,niter);% number of iterations% arriving r。

10、ate% set up storage);% interval time% arriving timefor i=1:niterrand( state,sum(clock) x=exprnd(lamda); n=1;while x=tn=n; elsen=n+1;endendr=normrnd(O.O5/253,O.23/sqrt(253),1,n); % generate n random jumps y=log(1.OE6)+cumsum(r);minX=min(y);% minmum return over next n jumpsbelow(i)=sum(minXO & a0 & a1。

11、5m=m+1;r=2\*binornd(1,p)-1;if r=-1a=a-1;elsea=a+1;endendif a=0t1(1,n)=m; m1=m1+1; elset2(1,n)=m; m2=m2+1;end endfprintf( The average times of arriving 0 and 10 respectively are %d,%d.n ,sum(t1,2)/m1,sum(t2,2)/m2);fprintf( The frequencies of arriving 0 and 10 respectively are %d,%d.n m2/N);,m1/N,m1/N,。

12、% verify:fprintf( The probability of arriving 0 and its approximate respectivelyare %d,%d.n, (p 0\*(1-卩)人5-p 人5\*(1-卩)人10)/(卩人5\*(卩人10-(1- p)。)，m1/N);fprintf( The expectation of arriving 0 or 10 and its approximate respectivelyare %d,%d.n,5/(1-2\* p)-10/(1-2\* p)\*(1-(1-卩)人5/卩人5)/(1-(1- plO/pTO),(sum(t1,2。

13、)+sum(t2,2)/N);.1通过Kolmogorov微分方程求转移概率%i续时间马尔可夫链输入：clear;syms pOO pO1 p10 p11 lamda mu; P= pOO, p01; p10, p11;Q=-lamda,lamda;mu,-muP\*Q输出:ans =-p 00\*lamda+p01\*mu, p 00\*lamda-p01\*mu-p 10\*lamda+p11\*mu, p 10\*lamda-p 11\*mu输入：p OO, pO1, p1O, p11=dsolve(D pO O=-pOO\*lamda+pO1\*mu,D pO仁 pOO\*lamda-pO1\*mu,D p1O。

14、=-p1O\*lamda+p11\*mu,D p1仁 p1O\*lamda-p11\*mu, pOO(O)=1, pO1(O)=O, p1O(O)=O, p11(O )=1)输出：pOO =mu/(mu+lamda)+ex p(-t\*mu-t\*lamda)\*lamda/(mu+lamda)pO1 =(lamda\*mu/(mu+lamda)-ex p(-t\*mu-t\*lamda)\*lamda/(mu+lamda)\*mu)/mup10 =mu/(mu+lamda)-ex p(-t\*mu-t\*lamda)\*mu/(mu+lamda)p11 =(lamda\*mu/(mu+lamda)+ex p(-t\*mu-t。

15、\*lamda)\*muA2/(mu+lamda)/muend% set the state of randn% p reallocate arrays .% for efficie ncydW(1) = sqrt(dt)\*ra ndn;W(1) = dW(1);for j = 2:NdW(j) = sqrt(dt)\*ra ndn;W(j) = W(j-1) + dW(j); end% first app roximati on outside the loop % si nee W(0) = 0 is n ot allowed% gen eral in creme ntplot(0:dt:T,0。

16、,W,r-)% plot W agai nst txlabel( t, FontSize ,16)ylabel( W(t),FontSize,16,Rotatio n,0)% BP ATH2 Brow nian p ath simulatio n: vectorizedrandn( state ,100) T = 1; N = 500; dt = T/N;% set the state of ra ndndW = sqrt(dt)\*ra ndn (1,N);W = cumsum(dW);% in creme nts% cumulative sumplot(0:dt:T,0,W,r-)% plo。

17、t W agai nst txlabel( t, FontSize ,16)ylabel( W(t),FontSize,16,Rotatio n,0)ll -0.5W(t)-0.5 E\*00.10.20.30.40.50.60.70.80.91t% BP ATH1 Brow nian path simulatio n: for randn( state ,100)T = 1; N = 500; dt = T/N;dW = zeros(1,N);W = zeros(1,N);%BP ATH3 Fun ction alo ng a Brow nia n pathrandn( state ,100)。

18、T = 1; N = 500; dt = T/N; t = dt:dt:1;% set the state of randnM = 1000;dW = sqrt(dt)\*ra ndn (M,N);W = cumsum(dW,2);U = exp(rep mat(t,M 1) + 0.5\*W);Umea n = mean( U);plot(0,t,1,Umea n,b- ), hold onplot(0,t,o nes(5,1),U(1:5,:),r-), hold% M p aths simulta neously% in creme nts% cumulative sum% plot mea。

19、n over M p aths off % plot 5 in dividual p athsxlabel( t , FontSize,16)ylabel( U(t), FontSize,16, Rotation ,0, HorizontalAlignment , right)lege nd( mea n of 1000 paths , 5 in dividual paths,2)aveerr = norm( (Umea n - exp( 9\*t/8),inf )% sample error%输出:5.5mean of 1000 paths5 in dividual p aths4.53.5U(t) 32.51.5.-.L - A0.5 I11C1\*00.10.20.30.40.50.60.70.80.91taveerr = 0.0504。