I know the following question is an often asked question on this website, but I still don't really catch it...
If $\tau_1$ and $\tau_2$ are stopping times, then how can I interpret the sum of $\tau_1$ and $\tau_2$ or there product? How do I know intuitively that the sum of two stopping times is still a stopping time, but the product of them is not? Could you give me an example from real life?
I know stopping time is a random variable, and I interpret it as a "time", when an event happens and in the moment when it happens I can decide that it has actually happened or not. I can decide it in the moment when it happens, so I don't need to wait or see into the future to know it has happened. Perhaps this explanation a little bit confused and not "well defined", but I hope you get what I mean...