Module 4:Renewal Processes and Theory, Limit theorems in renewal theory

  Lecture 17:Limit Theorems
 


Wald's equation

An integer valued random variable (r.v) is said to be a stopping time for a sequence  if the
event  is independent of , ,… for all . Thus one would observe  in a sequential order where  (remember it is a random variable (r.v)) denotes the number observed before one stops. Thus if , then we have observed  and not observed

Let us illustrate this concept of stopping time with an example.

Example 4.5
Consider ,  be independent such that , .Assume that we have , then this  is a stopping time. Example can be when we keeping flipping an unbiased coin and stop the experiment the moment the number of tails is 7.