I was reading your notes on stochastic calculus and I was wondering if there is an expression for the Riemann integral (with respect to t) of a Poisson Process or Compound Poisson Process? What is this integral equal to?

Is it also true (by Fubini Theorem) that the expectation of this integral is equal to the integral of the expectation?

Thank you.

Sincerely,

Alex. ]]>

The latter integral is in the Lebesgue sense — which is equivalent to the Riemann sense if the paths of are Riemann integrable (but that is not a requirement).

]]>thank you very much for your notes. I have a question. If we consider the Ito’s Isometry for the Brownian Motion then we will have expected value of squared stochastic integral is equal to the expected value of the integral of the squared function. Is the latter integral in the Riemann or Lebesgue sense?

Thank you.

Sincerely,

Alex. ]]>