Stochastic processes -

allandmunja · **Joined:** Sun, 3 Apr 2011 22:54:45 UTC **Posts:** 1

Hey guys! I was working with with a couple of stochastic problems and found myself in a corner.

I have two Exponential processes ( $N_t^{(1)}$ and $N_t^{(2)}$ )with intensities $\lambda_1$ and $\lambda_2$ respectively. Now suppose $N_0^{(1)}=2$ amd $N_0^{(2)}=1$ . What is probability that $N_t^{(1)}=5$ comes quicker than $N_t^{(2)}=5$ ?

I have reformulated this problem as follows: calculate $P(T_5^{(1)}<T_5^{(2)})$ It appears I can calculate this, but now I have noticed that probably I should use conditional probability conditioning on the initial values (two conditions). If that's right how can I solve the problem? Could someone give me a hint?

S.O.S. Mathematics CyberBoard

Stochastic processes -

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