Thread: Problem in martingale.

(Xn, Bn)n>=0 is a martingale. Xn+1/Xn belong to L'. Prove that E(Xn+1/Xn) = 1.

I know that I have to use Conditional expectation theory here, but i dont know how to proceed, though it looks to be a simple problem. If anyone know how to prove, please post the solution

Thanks

Hello,

What is Bn ?
And please please please, use the LaTeX... Not sure : is Xn+1/Xn the random variable Xn+1 conditioned on Xn ?

Bn is the filtration of the σ-algebra B of the space (Ω,B,P), and yes Xn+1 is conditioned on Xn.

Then I don't understand... Because is not always equal to 1...

that's just the question. please note that my question says that it belongs to the integrable space L'

I think the property that Xn is a sub σ-algebra of the filtration Bn must be used,then the answer is immediate. But I amnot sure.

Any i/p is appreciated.


Thanks in advance.