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 by
is a martingale known as Wald's martingale. [4] In particular, for all .
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. [1] [2] [3]
Wald's martingale can be seen as discrete-time equivalent of the Doléans-Dade exponential.
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 by
is a martingale known as Wald's martingale. [4] In particular, for all .
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