What Is the Martingale Property in Wald's Equation?

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SUMMARY

The discussion centers on the Martingale property in the context of Wald's equation, specifically regarding the sequence {S_n} defined as S_n = ∑_{i=1}^{n} Y_i, where Y_i are independent and identically distributed (iid) random variables with a finite mean μ. It is established that Z_n = S_n - nμ is a martingale under these conditions. The confusion arises from the definition of a martingale, which is crucial for understanding the proof of Wald's equation.

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Epsilon36819
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Hi everyone. I was going through a proof of Wald's equation, where it was claimed that if {S_n} is a sequence defined as S_n = \sum_1^{n} Y_i where the Y_i are iid with finite mean \mu, then Z_n = S_n - n \mu is a martingale.

But I don't see why... at all!

Help!
 
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Epsilon36819 said:
Hi everyone. I was going through a proof of Wald's equation, where it was claimed that if {S_n} is a sequence defined as S_n = \sum_1^{n} Y_i where the Y_i are iid with finite mean \mu, then Z_n = S_n - n \mu is a martingale.

But I don't see why... at all!

Help!

What definition of Martingale are you using?
 

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