Math341: Stochastic Modeling(No.11)
By Lin Yuanyuan
Apr. 27, 2011
Example 1. Let T be the time to extinction in the linear death process with
parameters X (0) = N and .
(a) Using the sojourn time view
Math341: Stochastic Modeling(No.4)
(Branching Processes)
By Lin Yuanyuan
Mar. 9, 2011
1. Key points.
Xn : the size of the n-th generation.
(n)
(n)
i : # of the ospring of i-th individual of the n-th g
Math341: Stochastic Modeling(No.3)
By Lin Yuanyuan
Mar. 2, 2011
1 (First-step Analysis) Key points.
Suppose cfw_Xn , n 0 is a Markov chain with state space cfw_0, 1, ., r 1, r, r +1, . . . N
where cf
Math341: Stochastic Modeling
By Lin Yuanyuan
Feb. 16, 2011
Review key points:
(1) Markov Process, Markov Chain (Markov process with discrete state space),
Discrete time Markov Chain, Continuous time M
Math341: Stochastic Modeling(No.13)
By Lin Yuanyuan
May 11, 2011
Key Points
(i). Elementary renewal theorem
M (t) =
t
+ o(t),
as t .
(ii). Rened renewal theorem
M (t) =
t
2 2
+
+ o(1),
22
as t .
(iii
Math341: Stochastic Modeling(No.10)
By Lin Yuanyuan
Apr. 20, 2011
Chapter 6: Continuous time Markov Chain
1. Key points.
(1). Pure birth processes.
Denition:(three postulates)
Xt is a CTMC with nondec
Math341: Stochastic Modeling(No.7)
By Lin Yuanyuan
Mar. 30, 2011
1. (The classication of states) Key points.
(1). Check whether or not a M.C. is irreducible by denition i j for all i, j .
(k )
Communi
Math341: Stochastic Modeling(No.6)
By Lin Yuanyuan
Mar. 23, 2011
1. (The long run behavior of M.C.) Key points.
(1). Two methods to check regularity.
Method 1: Denition.
If there exists a k > 0 such