Poisson process JP
20
Poisson 過程 1 http://www.slideshare.net/ShinjiNakaoka 授業レクチャーノート
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Transcript of Poisson process JP
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Poisson
1
http://www.slideshare.net/ShinjiNakaoka
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Bernoulli
2
(Bernoulli) n1 n-n1 () p=n1/n X=1 ()X=0 () ()
p =0.2 1 Bernoulli 10000 0 8000 1 2000
P.23-27
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3 P.23-27
(binomial) p Bernoulli n k
p =0.2 1 Bernoulli 10000
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Poisson
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Poisson Poisson
()
P.23-27
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5
N(t)
t: N(t):
Poisson
ATM etc
P.47-50
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6
(Levy flight)
(independent increments) t1
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Markov
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Markov MCMC (Markov Chain Monte Carlo)
t1
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8
Poisson Poisson
[] N(n)
n: N(n):
p (0
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Bernoulli p
t1
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10
t t nt=t [0,t] n p
[0,t] k t Poisson
P.47-50
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Poisson
11
[] f(h) h
(h>0)
P.50-55
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Poisson
12
[Poisson ] (counting) N(t)
(i)(ii)
(iii)
Poisson
[]
P.50-55
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Poisson
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Poisson () [0,t] k
[s,s+t] k
s t
(k )
P.50-55
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Poisson
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Poisson
Pk(t+h) (0,t], (t,t+h] Pk(t+h)
k Pk(t)
P.50-55
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Poisson
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Pk(t)
t Poisson
P.50-55
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[] (exponential) X
X X
=1 ) ATM
P.28-33
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[] (Gamma) X
X Gamma Gamma
=1, k=3 ) mRNA
P.28-33
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X1 () XN (N-1) N
0 N ():
Gamma
P.56-58
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[] Snn
P.56-58
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Poisson
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Poisson
(counting) N(t)
(i)
(iii)
(Vi)
(t) Poisson
(ii)
Gillespie Poisson
P.56-58
