How to express Jump Process in terms of the generator (rate matrix) A

dyh

Hi Guys

I have problem to express the jump process as following ways.

Please let me know your ideas~!!

Thank you so much.

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Let (Xt)t≥0 be an irreducible continuous-time jump process on a nite state space
{1,....,N}. Let T = inf{t > 0 : Xt ≠ X0} be the time of the first jump. Assuming
that α(1,2) > 0 express P(T > t|X0 = 1, XT = 2) in terms of the generator (rate
matrix) A

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