Let S n be a simple symmetric random walk; Let Y be a bounded symmetric random variable that takes values only in Z. (Y being symmetric means that Y and −Y have the same law.) Does there necessarily...

Let S_n
be a simple symmetric random walk; Let Y be a bounded symmetric random variable that takes values only in Z. (Y being symmetric means that Y and −Y have the same law.) Does there necessarily exist a stopping time N such that SN and Y have the same law? Why or why not?

Chapter 16