Recent content by osprey

  1. O

    Graduate Does E(e^{-X}) = 0 imply X = \infty almost surely for X \geq 0?

    Does the following make sense: E(e^{-X}) = 0 \Rightarrow X = \infty\quad a.s. ? (Intuitively yes, but mathematically?) Thank you in advance for your help! :-) /O
  2. O

    Graduate Why Is It Acceptable to Interchange Sum and Integral for Martingale Proof?

    Let M_t = \sum_{i=1}^\infty \frac{1}{i} (N_t^i - \lambda t) where \{ N^i \} is a sequence of iid Poisson processes with intensity \lambda . It can be shown that the series converges in the L^2 sense. Why is it ok to write \int \left ( \sum_{i=1}^\infty \frac{1}{i} (N_t^i - \lambda t)...
  3. O

    Graduate Diffeomorphisms and embedded submanifolds

    The tex-code in my post was behaving really weirdly - some parts of the code seemed to have "exchanged places", so I chose to delete what I had written. I apologize for the inconvenience...