1
vote
2answers
212 views

Looking for a limit related to the series in a previous post

Can any one show that the following limit? $$ \lim_{z\rightarrow \infty} \sqrt{z} \: e^{-z}\sum_{k=1}^\infty \frac{z^k}{k! \sqrt{k}} \quad \stackrel{?}{=} \quad\sqrt{2}-1. $$ If one uses the ...
9
votes
2answers
2k views

Convergence and non-convergence of left-point and mid-point Riemann sums

In standard calculus it is a well known fact that left-point and mid-point Riemann sums do become equal in the limit. When it comes to stochastic integration this is no longer the case. Taking the ...
6
votes
5answers
2k views

Discrete version of Ito's lemma

Could anyone give me some references where I could find (a) discrete version(s) of Ito's lemma (b) a proof how it converges to the continuous form in the limit (c) its usage within stochastic ...