I was working through a paper by M. De Donno, which proves the Ansel-Stricker lemma in a different way. The paper can be found here. I've chosen this paper instead of the original one by Ansel-Stricker, simply because my French is to bad. Reading this paper I have some question concerning the proof of Theorem 1.
- Why is it needed that $\sum_n P(\tau_n< T)<\infty$. This looks like Borel-Cantelli, but I do not see where we use this.
- How do I derive the bound for $(\Delta X^n_{\sigma_m})^-$?
- Why is $M^n_{t\wedge \sigma_m}\ge \theta_m-1-(m-\theta_m)$ and why is this positive? Or why do we need this calculation?
Thank you for your help.
hulik