Markov

1

http://www.slideshare.net/ShinjiNakaoka

Poisson

2

Poisson Poisson

()

P.23-27

Poisson

3

[Poisson ] (counting) N(t)

(i)(ii)

(iii)

Poisson

[]

P.50-55

Markov

4

Markov MCMC (Markov Chain Monte Carlo)

t1

Markov

5 P.79-80

(Markov ) () n Markov pij (transition probability)

) pij n ()

6 P.80-81

Markov

7 P.81-85

Markov Markov

X(0)=i0 i1,i2,,in

8 P.81-85

9 P.81-85

n i j n

1 n=0

n=0

1

10 P.81-85

n r (0rn) k n-r j k(k=0,1,2,) k

(Chapman-Kolmogorov )

11 P.81-85

() P(1)

Chapman-Kolmogorov

P Chapman-Kolmogorov Markov n

12 P.81-85

n j

n

13 P.87-89

i n n (first passage probability)

fij0=0 fij1=pij fijn i,j

i j ()fii=1 i (recurrent)fii

14 P.87-89

i

i

()fii=1 i (recurrent)fii

15 P.87-89

i Markov

(0

16 P.87-89

n

(Markov )

(Markov )

p=1/2 Markov (one-dimensional symmetric random walk)

Markov

17 P.101-102

i=0,1,2,

0t1

18 P.101-102

Markov Pij(t) Markov

Chapman Kolmogorov Markov Chapman Kolmogorov Pij(t) Pij(t)