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
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)...
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...