2
votes
1answer
143 views

Is $\lim_{n \rightarrow \infty}\sum_{k=0}^{n} \frac{|(1-\frac{n p_n}{n})|^{n-k}- e^{- \lambda}|}{k!}=0$?

I am currently the convergence of different processes. Doing this, I ended up with this expression and was wondering whether it is true that$$\lim_{n \rightarrow \infty}\sum_{k=0}^{n} ...
17
votes
3answers
1k views

Do convex and decreasing functions preserve the semimartingale property?

Some time ago I spent a lot of effort trying to show that the semimartingale property is preserved by certain functions. Specifically, that a convex function of a semimartingale and decreasing ...
2
votes
2answers
850 views

Examples of deterministic processes of quadratic variation which are of unbounded variation

In [Föllmer 81] (English translation to be found here) writes: "The class of processes of quadratic variation is clearly larger than the class of semimartingales: Just consider a deterministic process ...
9
votes
2answers
521 views

Inequality in Gaussian space — possibly provable by rearrangement?

The following problem arose for my collaborators and me when studying the computational complexity of the Maximum-Cut problem. Let $f : \mathbb{R} \to \mathbb{R}$ be an odd function. Let $\rho \in ...