Hi,my memories about stoch. calculus with jumps are quite weak, so I have a simple question.Assume a process of the kind:[$]d x_t = -a x_t dt + J_t dN_t[$]where[$]J_t[$] is an iid r.v. and [$]N[$] is Poisson with intensity [$]\lambda[$].Now, consider a simple transformation: [$]Y =\exp(m + q x)[$]The dynamics of Y is something like:[$]dY/Y = (...)dt + (e^{q J_t}-1)dN_t[$] Now, if I want to compute the "variance" of the growth rates of [$]Y[$] is it correct to measure it as follows?[$]\lambda E[(e^{q J_t}-1)^2]=\lambda (\phi(2q) -2 \phi(q) +1)[$]where I compute the expectation over the distribution of [$]J_t[$] by means of the laplace transorm [$]\phi(u)[$].Is this a correct measure of variance?Thanks a lot.

Yes, it is the variance 'rate', with the proviso that your [$]\phi(u)[$] is not really a LT but a mgf

Please excuse an off topic question: what is a basic textbook that discusses SDE's with jump terms, i.e. terms like [$]+J_t dN_t[$]

I'm not sure about that, but your question jogged a memory. If memory serves, when first learning about jumps, I founda highly cited 1972 Berkeley dissertation "A martingale approach to point processes" (Bremaud) quite helpful.I think I had to contact the library there for a copy, which is a standard service of theirs.