by quenderin
Last Updated October 10, 2019 05:20 AM

Consider a Gaussian random process $x(t)$ with some two-point correlation function $\xi$. Suppose $x(t_i) = u, t_i \in I$ for some set of points $\{t_i\}$. Define the function

$$ M_I(x,u) = \sum_{i} |x'(t_i)| $$

What can be said about the mean and variance of $M_I$? This is very close to Rice's formula and all the work on level crossings. I think I know how to compute the mean following the proof of Rice's formula, but the variance seems much harder.

Updated March 07, 2017 08:20 AM

Updated February 23, 2018 21:20 PM

Updated October 12, 2019 09:20 AM

- Serverfault Query
- Superuser Query
- Ubuntu Query
- Webapps Query
- Webmasters Query
- Programmers Query
- Dba Query
- Drupal Query
- Wordpress Query
- Magento Query
- Joomla Query
- Android Query
- Apple Query
- Game Query
- Gaming Query
- Blender Query
- Ux Query
- Cooking Query
- Photo Query
- Stats Query
- Math Query
- Diy Query
- Gis Query
- Tex Query
- Meta Query
- Electronics Query
- Stackoverflow Query
- Bitcoin Query
- Ethereum Query