Martingale in discrete time: Square integrable martingale

[WMD]

Does there exist a C < ∞ such that [imath] \mathbb{E}[M^2_n][/imath] ≤ C for all n?

Can we use the following proposition to answer this question? If yes, how can we use it?

If no, what would be correct answer to this question?

 

[Quasar Chunawala]

I could be wrong, but I think E[X_j^2] = 4 (1/3) + (1/4)(2/3) = 3/2. Since X_j's are independent, the expectation of M_n^2 is (3/2)^n which is unbounded.

 

[WMD]

I could be wrong, but I think E[X_j^2] = 4 (1/3) + (1/4)(2/3) = 3/2. Since X_j's are independent, the expectation of M_n^2 is (3/2)^n which is unbounded.

Thanks for your good attempt. Your answers looks reasonably correct.
Chat.G.P.T. gave the following answer.

Answered by Chat.G.P.T.
Answered by Chat.G.P.T.
What is your opinion about this answer?

 

[Quasar Chunawala]

In general, I think it just strings together some fragments that make grammatical sense in a coherent way, . It is still a stochastic parrot, as far as mathematical logic and reasoning are concerned.

 

[WMD]

In general, I think it just strings together some fragments that make grammatical sense in a coherent way, . It is still a stochastic parrot, as far as mathematical logic and reasoning are concerned.

My answer to this question: