Mathematics · Stochastic Processes
Let (N t 1 ) and (N t 2 ) be two independent Poisson processes with intensities a and b respectively, with a > b. Let M t = max{N t 1 , N t 2 } and X t = max(N t 1 - N t 2 , 0). Then which of the following is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1M is a pure birth process with birth-rate a + b
- 2M is a Poisson process with intensity max(a, b)
- 3X is a birth-and-death process with birth-rate a and death-rate b✓
- 4X is a Poisson process with intensity a - b
Correct answer
X is a birth-and-death process with birth-rate a and death-rate b
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