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B C
D 3 t
4 5
6 7
8
(1)
E ξt = aBt + 0 bWt
F t 2Y3`4a5
6 7Y8t
c
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4.ηt=Bt+ct d Ia<0
0 τ=inf{t>0;ηt∈/(a,b)}, @d`5.s
0,Bt>0)=4+2πarcsint. ¥¦Q- 6j.klmnoduep{0r,1"}Dsftg qtp Iq01=(t)p −q00(t) (r"5c=λ,q10=−q11= µ, h i Kolmogorov
7. (a) s Q- t {Xt} rwtuv00{ξn}, wx 11 {ξn} 2yzD
H {Xt} F{|2yG ziD' X~ W(b)EcD}) qM/ M/1~
D "
5 ve-first-served
(1) e-first-served.
(2)
(3)
8.{~
1,2,···,N}xDQ-twP(t)=(pij(t)).`t>
0, '~det(P(t))>
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1 5¨©¡cdHµ.( 1¥)'
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2 c
1
10" #$%&'()0!
1B=B(t)23456789B=
0,EB=
0,Var(B)=t. I1. @ Wt
2 A Bt
B C
D 3 t
4 5
6 7
8
(1)
E ξt = aBt + 0 bWt
F t 2Y3`4a5
6 7Y8t
c
G H a 2.dbPeQ5R6S7T8UBVDWf(g2)hηti=pB()2t)q−rB("t)s2t3D4u5v678XWDb t f(x)=g(x),x∈(a,b);f(a)=c1,f(b)=c2. w12xDygcg(x)(a,b) c1,c2 d I2tXW3.V(t)=e−αtB(e2αt), EV(t)Cov(V(t),V(s)).V(t)() D5678w12c@
4.ηt=Bt+ct d Ia<0
0 τ=inf{t>0;ηt∈/(a,b)}, @d`5.s
0,Bt>0)=4+2πarcsint. ¥¦Q- 6j.klmnoduep{0r,1"}Dsftg qtp Iq01=(t)p −q00(t) (r"5c=λ,q10=−q11= µ, h i Kolmogorov
7. (a) s Q- t {Xt} rwtuv00{ξn}, wx 11 {ξn} 2yzD
H {Xt} F{|2yG ziD' X~ W(b)EcD}) qM/ M/1~
D "
5 ve-first-served
(1) e-first-served.
(2)
(3)
8.{~
1,2,···,N}xDQ-twP(t)=(pij(t)).`t>
0, '~det(P(t))>
0. 9. M/M/11D2P(oisson ¡uλ;¢£¢¤( "
1 5¨©¡cdHµ.( 1¥)'
S TU
V )n¦hªD(uq n+
1 §n+2"5W(
2 ) ¥ ~ D n+ 2«®¯ l ° '2w¬±²Wx ³ §5´ ®µ¶ D2¬³5·¸
W «¹Uµ ¶10.cÂp Uµ¶D®º'ÃÄAÅÆ
D µ80 ¶»cÃ
2 Ä00 »U¼µ¶«½Ç" 5 cF¾2f Pois¿son®À'¬ Á iº λ100 È »È ¼ « ½ "
5 cÉ Å 30 ¹ x ÊË Ì
D Í Î
X , d
E exp(aX ), w 1
1 a
2 c
1
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