2. Consider the Markov jump process with generator matrix 1 0 0 −1 1 1 0 −1 0 0 2 -4 2 1007 0 0 0 0000 0 0 0 1 -2 1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 and let (P(t)) be the associated transition semigroup. Find lim→∞ P(t). [10] Hint: find the communicating classes and their hitting probabilities.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. Consider the Markov jump process with generator matrix
1
0
0
−1
1
1
0
−1
0
0
2 -4 2
1007
0
0
0
0000
0
0
0
1 -2 1 0
0
0
0
0
0
-1 1
0
0
0
0
0 0
0
and let (P(t)) be the associated transition semigroup. Find lim→∞ P(t). [10]
Hint: find the communicating classes and their hitting probabilities.
Transcribed Image Text:2. Consider the Markov jump process with generator matrix 1 0 0 −1 1 1 0 −1 0 0 2 -4 2 1007 0 0 0 0000 0 0 0 1 -2 1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 and let (P(t)) be the associated transition semigroup. Find lim→∞ P(t). [10] Hint: find the communicating classes and their hitting probabilities.
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