I always seem to have troubles when it comes to proving an integrability condition of a particular process... somehow I don't have the right method.
I have the following stochastic process:
M(t) = N(t) - kt
Where N(t) is a poisson process of parameter kt.
M is called a compensated poisson process.
I want to prove that: E[ | M(t) | ] < +infinity (in other words, that it is finite).
I have searched for a while, and all my attempts have been infructuous.
Thank you for your help.