Wald's martingale
In probability theory, Wald's martingale is the name sometimes given to a martingale used to study sums of i.i.d. random variables. It is named after the mathematician Abraham Wald, who used these ideas in a series of influential publications.
Wald's martingale can be seen as discrete-time equivalent of the Doléans-Dade exponential.
Formal statement
Let be a sequence of i.i.d. random variables whose moment generating function is finite for some, and let, with. Then, the process defined byis a martingale known as Wald's martingale. In particular, for all.