Timeline for Quadratic Variation of a Martingale in Hlibert Spaces
Current License: CC BY-SA 3.0
9 events
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| Jun 15, 2015 at 14:05 | comment | added | user2379888 | The Pisier notes look useful, thanks. Related question, does anyone know a reference for Martingale convergence in finite dimensional vector spaces? I realized I couldn't immediately locate one. | |
| Jun 15, 2015 at 7:14 | comment | added | Bill Johnson | You might take a look at Pisier's course notes on martingales in Banach spaces: webusers.imj-prg.fr/~gilles.pisier/ihp-pisier.pdf | |
| Jun 15, 2015 at 6:01 | comment | added | Nate Eldredge | I guess I don't know specifically, but often one can prove such things (assuming your Hilbert space is separable) by letting $P_k$ be a sequence of finite-rank orthogonal projections with $P_k \to I$ strongly, proving something for the finite-dimensional process $P_k M_n$ with uniformity in $k$, and letting $k \to \infty$. | |
| Jun 15, 2015 at 2:48 | comment | added | user2379888 | I'm interested in what I think is a simpler problem. My process is discrete in time, and those works appear to handle the continuous case. | |
| Jun 15, 2015 at 2:35 | comment | added | Nate Eldredge | We proved a few basic results along these lines in this paper, and one place to look for more material on Hilbert space-valued martingales is Métivier's book Semimartingales. If this seems to be helpful I can add it as an answer. | |
| Jun 15, 2015 at 2:22 | history | edited | user2379888 | CC BY-SA 3.0 |
added 99 characters in body; edited title
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| Jun 15, 2015 at 2:21 | comment | added | user2379888 | Yes, I am working in a Hilbert space. I've edited to add some more details. | |
| Jun 15, 2015 at 2:13 | comment | added | Nate Eldredge | Intuitively, quadratic variation seems more likely to be a useful object if you are working in a Hilbert space. | |
| Jun 14, 2015 at 22:26 | history | asked | user2379888 | CC BY-SA 3.0 |