tea.mathoverflow.net - Discussion Feed (Doob's inequality)2019-12-11T22:46:01-08:00http://mathoverflow.tqft.net/
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George Lowther comments on "Doob's inequality" (20823)http://mathoverflow.tqft.net/discussion/1487/doobs-inequality/?Focus=20823#Comment_208232012-12-14T14:31:35-08:002019-12-11T22:46:01-08:00George Lowtherhttp://mathoverflow.tqft.net/account/502/
Yes, I agree that this is not really suitable for mathoverflow, and is more likely to get an answer at math.stackexchange. Also, the inequality mentioned is a special case of the following question ...
Yes, I agree that this is not really suitable for mathoverflow, and is more likely to get an answer at math.stackexchange. Also, the inequality mentioned is a special case of the following question (and answer) already asked on math.SE http://math.stackexchange.com/q/88371/1321, and the technique is to use time-change.
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HJRW comments on "Doob's inequality" (20821)http://mathoverflow.tqft.net/discussion/1487/doobs-inequality/?Focus=20821#Comment_208212012-12-14T13:55:56-08:002019-12-11T22:46:01-08:00HJRWhttp://mathoverflow.tqft.net/account/98/
To clarify, I think MemT is asking if this question could be reopened. As s/he has explained that s/he's revising for an exam, I have explained that this is not on-topic for MO and recommended ...
To clarify, I think MemT is asking if this question could be reopened. As s/he has explained that s/he's revising for an exam, I have explained that this is not on-topic for MO and recommended math.stackexchange.com.
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MemT comments on "Doob's inequality" (20818)http://mathoverflow.tqft.net/discussion/1487/doobs-inequality/?Focus=20818#Comment_208182012-12-14T13:03:31-08:002019-12-11T22:46:01-08:00MemThttp://mathoverflow.tqft.net/account/856/
Hey. Could anyone tell me if I have a process $I_t=\int_0^t f_tdB_t,$ where $(f_t,t\ge 0)$ is bounded, $|f_t|\leq M$ almost surely for all $t \ge 0$, how can I show that ...
$$\mathcal{P}\left[\sup_{0\leq t\leq T}|I_t|>\lambda\right]\leq \exp\left(-\frac{\lambda^2}{2M^2T}\right).$$

First I tried by defining $Y_t^{\alpha}=\exp\left(\alpha I_t-\frac{1}{2}\int_{0}^t f^{2}(s)ds\right)$, where $\alpha\in \mathbb{R}$ to get an upper bound. But I need to know how to show that $Y_t^{\alpha}$ is a mgale. Thank]]>