How to find out if a stochastic process is martingale?
I used Ito's formula to prove it is not a martingale. Can it be a supermartingale?
How to use Jensens inequality to find if a process is martingale?
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1Presumably ${S(t): t\in\text{some set ($\mathbb R^+$ or $\mathbb N$ or $\mathbb R$?)}}$ is some stochastic process, but which one? $\qquad$ – Michael Hardy Jul 10 '16 at 21:23
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1Is $S_t$ a arbitrary stochastic process? $dS_t=?$ – Behrouz Maleki Jul 10 '16 at 21:39
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1Hint: Jensen's inequality. – Math1000 Jul 10 '16 at 22:49
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Is it true that the above process is not martingale? I just want make sure. – flyhigh1 Jul 10 '16 at 23:32
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In order to be able to answer this question, we need to know what $S(t)$ is, as @BehrouzMaleki already pointed out. Also in order to use Ito's formula to show it is not a martingale, one needs to know what $dS_t$ is, and hence again what $S(t)$ is. Also, please don't edit your question in such a way that the original context is lost. You deleted so much that I had no idea what you are asking. Now I have a better idea, but still don't know until you specify what $S(t)$ is. As of now the question is too vague to have any definitive and non-speculative answer. – Chill2Macht Jul 19 '16 at 00:54
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Also this might have been asked and unanswered before: http://math.stackexchange.com/questions/1857725/is-the-logst-function-martingale, although if it is it doesn't matter since the other question has not been answered. Is your $S(t)$ the same as in this question? – Chill2Macht Jul 19 '16 at 01:00