1
$\begingroup$

How is $I_{[0,\infty)}(t)$ defined? This must be a notation in probabilty theory.

  • 0
    Although indicator functions come up in probability, it doesn't seem that an indicator over an infinite interval would come up.2012-07-04

1 Answers 1

1

You can use the Heaviside Step Function $H(t)$:

$H(0) = 1$ is used when $H$ needs to be right-continuous. For instance cumulative distribution functions are usually taken to be right continuous, as are functions integrated against in Lebesgue–Stieltjes integration. In this case $H$ is the indicator function of a closed semi-infinite interval: $ H(t) = \mathbf{I}_{[0,\infty)}(t).\, $

  • 1
    ...or one could use Iverson brackets as well: $[t \geq 0]$.2012-08-09