Timeline for Schilder's theorem for brownian bridges
Current License: CC BY-SA 4.0
8 events
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| Sep 27, 2018 at 6:31 | comment | added | leo monsaingeon | Aaaaaaah, I see. Thanks Nate, this clears things up. Again, sorry for my limited understanding of probabilistic notations/definitions, indeed centered Gaussian measures cover the case of my bridge $R^{\nu,x,y}$. | |
| Sep 26, 2018 at 22:13 | comment | added | Nate Eldredge | It's an arbitrary centered Gaussian measure, which includes the law of any continuous mean-zero Gaussian process. Brownian bridge which starts and ends at zero is certainly such a process. | |
| Sep 26, 2018 at 20:36 | comment | added | leo monsaingeon | Thank you Nate for your time. I could get my hands on the 1998 version of Bogachev's book, but as far as I can see his corollary 4.9.3 deals with standard Brownian (centered Gaussian, i-e brownian started from $0$) and not with the bridges. But the book is quite dense so it's hard to navigate through all the notations and perhaps I missed a point? | |
| Sep 26, 2018 at 13:54 | comment | added | Nate Eldredge | I think that Corollary 4.9.3 of Bogachev's Gaussian Measures may be what you want. It certainly covers the case $x=y=0$. The rate function is going to come from the Cameron-Martin norm for Brownian bridge which I don't recall off the top of my head. For further references, see the bibliographic notes at the bottom of page 385. I will try to post more later if I have time. | |
| Sep 26, 2018 at 9:56 | history | edited | leo monsaingeon | CC BY-SA 4.0 |
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| Sep 26, 2018 at 9:13 | history | edited | leo monsaingeon | CC BY-SA 4.0 |
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| Sep 26, 2018 at 8:59 | history | edited | leo monsaingeon | CC BY-SA 4.0 |
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| Sep 26, 2018 at 8:52 | history | asked | leo monsaingeon | CC BY-SA 4.0 |