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Unformatted text preview: A and B . 5. Let p k ( t, s ) = X tX s , where X t is a homoegenous Poisson counting process with rate Î» . Show that the diÂ²erential equation âˆ‚ âˆ‚t p k ( t, s ) = Î» [ p k1 ( t, s )p k ( t, s )] is solved by p k ( t, s ) = eÎ» ( ts ) ( Î» ( ts )) k k ! k = 0 , 1 , . . . , t > s â‰¥ . 1 6. Let p k ( t, s ) = X tX s , where X t is an inhomoegenous Poisson counting process with timevaryng rate Î» t . Show that the diferential equation âˆ‚ âˆ‚t p k ( t, s ) = Î» t [ p k1 ( t, s )p k ( t, s )] is solved by p k ( t, s ) = eÎ» R t s Î» x dx ( R t s Î» x dx ) k k ! k = 0 , 1 , . . . , t > s â‰¥ . 2...
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 Spring '08
 Stites,M
 Pk, Probability theory, Stochastic process, Xt, Xt âˆ’ Xs

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