(2.4.1)--随机过程-均方连续均方可微2019-7-16.pdf

1、CONTENTS T t X(t),(t)EX2 0lim 020ttE X t-X t=T t),t(X 0t T t T T t),t(X 00ttl i m X t=X t T t X(t),0t),(),(lim)t(X)t(X m i l0 0 2 1,0t t0 2 1 0t t t tt t t 1 2 01 2 0 0t,t tlim(t,t)(t,t)2EX t :)X(t EX(t lim),(lim2 1,2 1,0 2 1 0 2 1t t t t t tt t),()(t X)()(0 0 022 10 2 0 1t t E t X m i l t X m i l E

2、t t t t 01 2 020tt1 0 2 0t,t tE X t-X t=E X t-X t X t-X tlimlim 1 2 0 2 0 1 01 2 2 0 1 0 0 0t,t t t t t tlim t,t lim t,t lim t,t+t,t=0 T t X(t),(t)EX2 ht X h t X)()(m i l0 h t)t(X X(t)0 hX t+h-X tX t l i mh t t f(t)T t X(t),)()()()()()(t X t f t X t f t X x f )()()()(lim0t mdtt dmht X h t XEh(1)h0X

3、t+h-X tm=E X t=E l i mh 11 2 1 21 1 2 2001 1 2 202121 2 1 2 1 2 1 2012011limlim()h hh,hhh t,t E X t X tX t h X t X t h X tE l i m l i mh hE X t h X t X t h X thh t,t t h,t h t,t h t h,t t,thh t t T t X(t),(t)EX20t12(t,t)12t=t=t 2,ht X h t X)()(m i l 0 h 00hhX t+h-X t X t+h-X tlimEhh1221212t=t=t(t,t)tt,