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Suppose I have a random walk $X_{n+1} = X_n+A_n$ where $A_n$ is an iid sequence, $\mathsf EA_n = A>0$. How to construct a martingale measure for this case?

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Edit: Albeit of BFin or entry MFE type, sounds like homework.Answer: In many ways, for example take the countable product of (.-E[A])*(lawofA). More generally if g(x,y) is a function such that E[g(A,E[A])]=0 then g(.,E[A])*lawofA will do. Of course it doesn't have to be equivalent, like if A is deterministic.

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what should I do if $A$ say $\mathcal N(1,1)$? – Ilya Jun 23 '11 at 17:41
For g, you could use an Hermite polynomial of random (independent) degree, applied to A-1. Use it to pushforward the law of A countably many times. Construct the limit of this compatible system.Finally apply your measurable mapping: Xn+1=Xn+An. X is a martingale. Btw is this homework?The question is useless because too vague: specifying probability space and filtration would help. – imateapot Jun 23 '11 at 18:54

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