Timeline for Expected value of a stochastic integral expression
Current License: CC BY-SA 3.0
14 events
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| Nov 27 at 0:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 30 at 0:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 1 at 3:14 | comment | added | tsnao | By the way, it's not true that $\mathbb{E} \int_0^X e^{bs} dB_s = 0$ for general X. Let, for example, $X = \inf \{ t > 0 : B_t = c \}$. Then with $b = 0$, we have $\mathbb{E} \int_0^X dB_s = \mathbb{E} B_X = c \neq 0$. Even if $X$ is bounded, this may easily be false, let $X = \min \{ t \in [0, T] \colon B_t = \max_{s \in [0, T]} B_s \}$. Then $\mathbb{E} \int_0^X dB_s = \mathbb{E} B_X = \mathbb{E} |B_T| \neq 0$. | |
| Mar 31 at 23:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 2, 2023 at 22:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 4, 2023 at 21:08 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 6, 2023 at 21:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 7, 2022 at 20:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 7, 2022 at 19:10 | answer | added | Thomas Kojar | timeline score: 0 | |
| Feb 20, 2015 at 15:40 | history | edited | lkdo | CC BY-SA 3.0 |
changed bracket notation around the expectation
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| Feb 20, 2015 at 15:39 | comment | added | lkdo | @Nate Yes, the angle brackets are used as parenthesis for the expectation. I'll change them to square brackets. I see now how $X$ needs to be specified a more. I am looking into hitting times for SDEs, in particular the Ornstein-Uhlenbeck $dY(x) = (ax+b)dx + \sigma dW(x)$ because it has an explicit solution. The random variable X is defined as the values x for which Y(x)=y. First exit times can be studied via the Backward Kolmogorov with specified region boundaries, but I was wondering if some information about hitting times (not "first" anymore) can be obtained directly from the SDE solution. | |
| Feb 20, 2015 at 15:19 | comment | added | Nate Eldredge | What do the angle brackets inside the expectation denote? Usually angle brackets would mean "quadratic variation" but that doesn't seem to make sense here. Are you just using them as parentheses? Anyway, without knowing more about the random variable $X$ (such as how it relates to the Brownian motion) I don't see how one is going to be able to say anything. | |
| Feb 20, 2015 at 14:51 | review | First posts | |||
| Feb 20, 2015 at 16:16 | |||||
| Feb 20, 2015 at 14:41 | history | asked | lkdo | CC BY-SA 3.0 |