Non-martingale with respected to the natural filtration, and satisfies $E[M_{n+1} | M_n]=M_n$

Asked Jul 12 '15 at 14:03

Active Jul 12 '15 at 14:09

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I am thinking about the exercise:

Exercise 5. Give an example of a random sequence ($M_n$) such that $E[ M_{n+1} | M_n ] = M_n$ for all $n\ge0$, but which is not a martingale w.r.t. the filtration $F_n = \sigma(M_0, \dots , M_n)$.

From Exercise 5 of Link : http://www.math.bme.hu/~gabor/oktatas/SztoM/StModHW_2014.pdf

edited Jul 12 '15 at 14:09

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asked Jul 12 '15 at 14:03

Shangjie Yang

I want to give an example that satisfies E[M_n+1 | M_n]= M_n, but E[M_n+1 | M_n, ...., M_0]!=M_n – Shangjie Yang Jul 12 '15 at 14:09

Non-martingale with respected to the natural filtration, and satisfies $E[M_{n+1} | M_n]=M_n$

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