1
$\begingroup$

I have a little problem which is in part due to my lack in english skills. I am currently reading a book and I dont understand the following chapter (RW stands for random walk): part1
part2
The problem is i dont understand what the author means with $\lambda \in P(\mathbb{R})$ (the set of all probability distributions). What is a probability distribution? THe wikipedia article is not quite clear. Im not sure if $\lambda$ is a distribution function or a probability measure on R. Now up to this point The F and its n-th fold have been distribution functions. But the proof that a standard model always exists would imply that the F's and the $\lambda$ are probability measures now.

thanks in advance

$\endgroup$
  • $\begingroup$ Its quite clear that Im having a mathematical problem here. And not even wikipedia gives a clear definition, or rather both possibilities as a definition $\endgroup$ – StefanWK Dec 22 '17 at 12:03
  • $\begingroup$ In your link, both $\lambda$ and $F$ are probability measures. $\endgroup$ – fourierwho Dec 23 '17 at 22:36
-1
$\begingroup$

A probability distribution is a function F(x) defined on the real line with the following properties: $F(x)$ is monotone increasing, $\lim_{x \to -\infty}F(x)=0,\ \lim_{x \to \infty}F(x)=1$.

$\endgroup$
  • $\begingroup$ No. You are confusing the probability distribution (a measure, thus defined on a sigma-algebra) with its CDF (a function defined on the real line). $\endgroup$ – Did Dec 23 '17 at 22:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.