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question on compound poisson process
Posted: April 15th, 2008, 9:15 am
by bquant
Let's construct the compound poisson process as,where Y_n are iid r.v.I read from some notes that, for a function f(X_t),I am wondering why it is not
question on compound poisson process
Posted: April 15th, 2008, 12:58 pm
by Stale
Hi bquant..In your last line, the first equation would be correct for any Levy-process. As a matter of fact it is taken to be the definition of the jump at time t. I have not seen the second one, but it looks alright to me. Where exactly did you find this result?Regards,Stale
question on compound poisson process
Posted: April 15th, 2008, 1:21 pm
by bquant
Hi StaleI did not realize that the first line is the definition of the jump. I thoughtit is a derivation. I got the second line by an intuition, since I thoughtthe jump is from X(t-) to X(t-)+Y, If Y=1 const, that is pure jump process.Since X(t-) is right-cont, we will not have X(t-)=X(t), right? that meansthe two lines are not consistent.QuoteOriginally posted by: StaleHi bquant..In your last line, the first equation would be correct for any Levy-process. As a matter of fact it is taken to be the definition of the jump at time t. I have not seen the second one, but it looks alright to me. Where exactly did you find this result?Regards,Stale