Timeline for On stochastic integration
Current License: CC BY-SA 4.0
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| Nov 19 at 10:02 | 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. | |
| Jul 22 at 9:09 | 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. | |
| Mar 24 at 9:00 | 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. | |
| Feb 23 at 7:33 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Feb 23 at 5:51 | answer | added | Thomas Kojar | timeline score: 0 | |
| Nov 6, 2016 at 22:14 | comment | added | ithusiasm | I know, what you have written, but this does not answer my question. | |
| Nov 3, 2016 at 23:48 | comment | added | Liviu Nicolaescu | The problem appears when you want to integrate (against) discontinuous semimartingales, e.g. $X$ is a discrete time martingale. If $X$ is a continuous (local) semimartingale than $\int_0^t H(s) dX(s)$ makes sense for progressive processes. Also, replacing $t_i$ by $T_i$ is not that important, but it yields to faster proofs. Have a look at LeGall's recent book Brownian Motion, Martingales and Stochastic Integrals. | |
| Nov 3, 2016 at 17:25 | comment | added | ithusiasm | Right, but in Jacod/Shiryaev they argue that one needs predictibility in order to extend the stochastic integral beyond simple processes. They do not write: "predictibility is necessary in order to extend and stay in the (local) martingale world". | |
| Nov 3, 2016 at 16:44 | comment | added | Liviu Nicolaescu | For the integral $\int_0^t H(s) dB(s)$ to be a martingale, $H$ has to be predictable. Also, you may want to open vol.2 of the book Diffusions, Markov Processes and Martingales by Rogers and Williams. | |
| Nov 3, 2016 at 16:05 | history | asked | ithusiasm | CC BY-SA 3.0 |