Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am reading a paper and spot the following concept.

Given a sequence of random probability $p_n \in [0,1], n \in \mathbb N$ of some events, assume there exists a stochastic process $X: \Omega \times [0, \infty) \to \mathbb N$ and a $k \in \mathbb N$ and $$ p_n = \int_{n-1}^n I_{\{X(t)=k\}} dt $$ $X$ is said to be the kernel of $p_n$'s.

$I_{\{X(t)=k\}}$ looks like a density function, but not really.

Is there more information or reference so that I can learn more about the concept? Thanks!

share|cite|improve this question
It isn't exactly the same, but it reminds me of stochastic discount factors/pricing kernels in finance as here, too, the variable $X$ allows you to recover the information $p_n$. With the caveat of it not being exactly the same, there is a wiki article on this. – gnometorule Mar 3 '13 at 4:07

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.