Need help understanding this formula (monte carlo/poisson)

[supermario65]

Hi,

I'm having a little trouble understanding this little part from a paper. It's about monte carlo simulations, but that shouldn't really matter. First, there's this formula:

Fair enough. But then it states that this model can be adapted to the following:

But this new term should almost always be the same as the original one, since Poisson(0.01) almost always returns 0?

I'm pretty sure I'm interpreting the upper bound wrong, but what should it be then?

Thanks!

 

[lippyka]

The upper bound in the new model should be 1, not 0.01. Since Poisson(0.01) almost always returns 0, the upper bound is effectively limited to 1. This means that the model can be adapted so that it only considers outcomes up to a certain value, instead of all possible outcomes.