# Tagged Questions

**1**

vote

**2**answers

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 ...

**3**

votes

**2**answers

334 views

### How to integrate an exponential function of an exponential function?

Does any one know how to calculate the following integration?
$$
\int_{\mathbb{R}} \left(\exp(z \: e^{-y^2})-1\right)^2 dy=?,\quad z>0.
$$
This post is related to my previous question here , ...

**2**

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**2**answers

229 views

### What are the difference between modeling with stochastic differential equations (SDE) and ordinary differential equations (ODE) with a random force?

There are lots of differences between SDE and ODE. From the theoretical point of view an also from the numerical algorithms used for simulations. But I am interested in knowing if there is a point ...

**0**

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**0**answers

223 views

### Density of Dolean exponentials in L2 and Wiener Measure

Assume that W is the classical Wiener space C([0,1],R) note $\mu$ the Wiener measure, and denote by $\mu_s$ the image of $\mu$ under the maping $T: W ->W$ such that$ T(w)= \sqrt(s) w$ . Denote by ...

**10**

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**2**answers

522 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 ...