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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[Valkarie]

P(T > t|X0 = 1, XT = 2) can be expressed as the following: P(T > t|X0 = 1, XT = 2) = 1 - [α(1,2) * e^(-A*t)]/[1+(N-1)*α(1,2)*e^(-A*t)]