Lecture 13: Global Illumination and Path Tracing (82)

theandrewchan

The finiteness of the estimator is only in the expected number of recursive steps, right? Hypothetically if you got really unlucky with a constant $p_{rr}$ you could continue for an arbitrary number of steps.

raghav-cs184

Hi Andrew. If you think about convergence conditions in probability, the probability that you will continue for a non-finite number of steps converges to 0 in probability and almost surely!

The finiteness of the estimator is only in the expected number of recursive steps, right? Hypothetically if you got really unlucky with a constant $p_{rr}$ you could continue for an arbitrary number of steps.

Hi Andrew. If you think about convergence conditions in probability, the probability that you will continue for a non-finite number of steps converges to 0 in probability and almost surely!