The concept of a stopped martingale leads to a series of important theorems, including, for example, the optional stopping theorem which states that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial value.
The concept of a stopped martingale leads to a series of important theorems. Eg. the optional stopping theorem (or optional sampling theorem), that says, under certain conditions, that the expected value of a martingale at a stopping time is equal to its initial value.