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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.

  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.
  2. How do I derive the bound for $(\Delta X^n_{\sigma_m})^-$?
  3. 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

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    @ hulik : by the way the point (ii) of th 1 uses that $\eta_k$ converges stationarily to $T$. What does stationarily means precisely in this context ?2012-10-01
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    @TheBridge that's a good question! I was also unsure about that, since I've never heard this expression. I think it should mean stationary. If I look at Corollary 2 below of theorem 1, I guess it means monotone increasing2012-10-01
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    @ hulik : Iguess you are right, by the way I think I have figured out your point 1.2012-10-01

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