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

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

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