##  [Optional Stopping Theorem](/optional-stopping-theorem) 

  ##  [Optional Stopping Theorem](https://natural.quantumdictionary.io/optional-stopping-theorem-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A result in martingale theory stating that, under specified integrability or boundedness conditions on a stopping time τ and a martingale (M_t), the expectation at the stopping time equals the initial expectation: E[M_τ] = E[M_0].