随机过程(2013)-第三讲-article

《随机过程(2013)-第三讲-article》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、OutlineContents1111nnnùùù²²²•••‘‘‘ÅÅÅLLL§§§11.1‘ÅL§²•5...........................11.2°²•L§ƒ'¼ê†Ì—Ý...................81.3°²•L§õÇÌ—Ý.......................101.4‘ÅL§ˆ{²5........................171.5xD(‘ÅL§............................201.6....................

2、.................211111nnnùùù²²²•••‘‘‘ÅÅÅLLL§§§1.1‘‘‘ÅÅÅLLL§§§²²²•••555îîî²²²•••LLL§§§£££ddd²²²•••LLL§§§¤¤¤X(t)´˜‡‘ÅL§"XJé?¿2R§kž£ØC5FX(x1;:::;xk;t1;:::;tk)=FX(x1;:::;xk;t1+;:::;tk+)d/fX(x1;:::;xk;t1;:::;tk)=fX(x1;:::;xk;t1+;:::;tk+)K¡X(t)´˜‡î²•‘ÅL

3、§"élÑGL§§Œ^éÜVǼê5£ãPfX(t1)=x1;:::;X(tk)=xkg=PfX(t1+)=x1;:::;X(tk+)=xkgélÑžmL§§^VÇŸþ¼ê5£ã§êŠPfX(n1)=x1;:::;X(nk)=xkg=PfX(n1+)=x1;:::;X(nk+)=xkg~~~KKK3:1N(t)~~~3:1Poisson‘Å>&Ò£˜‡lÑGL§¤X(t)=X(0)(1)§Ù(t)kt¥N(t)´PoissonL§£PfN(t)=kg=e¤"k!1)PfX(0)=1

4、g=1=HXZhou2ž§X(t)´î²•‘ÅL§¶2)PfX(0)=1g6=1=2ž§-t!1§KX(t)ªu˜‡î²•‘ÅL§")))µµµÄky§X(t)´˜‡MarkovL§"PfX(tk+1)=xk+1jX(tk)=xk;X(tk1)=xk1;:::;X(t1)=x1g1(1+e2(tk+1tk));ifxPfN(tk+1tk)=eveng=k+1=xk=21(1e2(tk+1tk));ifxPfN(tk+1tk)=oddg=k+16=xk2=PfX(tk+1)=xk+1jX(

5、tk)=xkg1~~~KKK3:1

6、^MarkovL§5ŸÚþ¡VÇOŽúªÑPfX(t1)=x1;:::;X(tk)=xkg=PfX(t1)=x1gPfX(t2)=x2jX(t1)=x1g


PfX(tk)=xkjX(tk1)=xk1g±9PfX(t1+)=x1;:::;X(tk+)=xkg=PfX(t1+)=x1gPfX(t2+)=x2jX(t1+)=x1g


PfX(tk+)=xkjX(tk1+)=xk1g=PfX(t1+)=x1gPfX(t2)=x2jX(t1)=x1g

7、PfX(tk)=xkjX(tk1)=xk1g~~~KKK3:1þ¡üª«O3uÏfPfX(t1)=x1gÚPfX(t1+)=x1g"1)PfX(0)=1g=1=2ž§A^~2:11OŽúªŒPfX(t1)=x1g=PfX(t1+)=x1g=1=2“£c¡ü‡úª§ÑPfX(t1)=x1;:::;X(tk)=xkg=PfX(t1+)=x1;:::;X(tk+)=xkg=X(t)´î²•‘ÅL§"~~~KKK3:12)y3b½PfX(0)=1g=p6=1=2;PfX(0)=1g=1pu´£ùp

8、^/ªþØÓu~2:11OŽ{§•Œ±E^~2:11OŽ{¤N(t)PfX(t)=1g=PfXHXZhou(0)(1)=1g=PfX(0)=1;N(t)=Even_Numberg+PfX(0)=1;N(t)=Odd_Numberg£ŒŒ5¤=PfX(0)=1gPfN(t)=Even_Numberg+PfX(0)=1gPfN(t)=Odd_Numberg£¯‡Õá5¤p2t1p2t12t=1+e+1e=1+(2p1)e2222~~~KKK3:1¤±limPfX(t)=1g=

9、1=2t!1limPfX(t)=1g=11=2=1=2t!1000t¿©Œ§¦PfX(t)=1g1=2§KttžPfX(t1)=x1g1=2PfX(t1+)=x1g=1=2u´PfX(t1)=x1;:::;X(tk)=xkgPfX(t1+)=x1;:::;X(tk+)=xkg=X(t)•˜‡Cq‘ÅL§"îîî