Comments on: Quadratic Variations and the Ito Isometry
https://almostsure.wordpress.com/2010/03/29/quadratic-variations-and-the-ito-isometry/
A random mathematical blogWed, 12 Oct 2011 16:50:11 +0000
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By: Alex
https://almostsure.wordpress.com/2010/03/29/quadratic-variations-and-the-ito-isometry/#comment-923
Wed, 12 Oct 2011 16:50:11 +0000http://almostsure.wordpress.com/?p=516#comment-923Dear Almost Sure,
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.
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By: George Lowther
https://almostsure.wordpress.com/2010/03/29/quadratic-variations-and-the-ito-isometry/#comment-760
Sun, 01 May 2011 23:57:26 +0000http://almostsure.wordpress.com/?p=516#comment-760The 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).
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By: Alex
https://almostsure.wordpress.com/2010/03/29/quadratic-variations-and-the-ito-isometry/#comment-759
Sun, 01 May 2011 14:45:08 +0000http://almostsure.wordpress.com/?p=516#comment-759Dear Almost Sure,
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.
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