Timeline for Convergence and non-convergence of left-point and mid-point Riemann sums
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Mar 5, 2010 at 12:22 | comment | added | The Bridge | Ok ! Thank you George for your perfectly clear answer | |
| Mar 4, 2010 at 22:24 | comment | added | George Lowther | If X has finite p-variation and Y finite q-variation with 1/p+1/q=1, then you can use the Holder inequality rather than Cauchy-Schwartz in my argument above to get a bound on the correction term. If 1/p+1/q>1 then there will be no correction, and using a similar argument as with Riemann integration, the integral does exist. If 1/p+1/q <= 1 then we only have a bound on the correction term. There is no guarantee that the sum converges to a well defined integral but, if it does, there can be a correction correction term. | |
| Mar 4, 2010 at 17:45 | comment | added | The Bridge | I have an additional question, I think I can remember something about Rough Paths and Integration where by using something related the Young Integral you are able to define an integral over path of q-variations with q>1 and define some kind of differential calculus. I wonder if this kind of "integrals" have some correction terms like in Itô integral ? Regards | |
| Mar 1, 2010 at 5:54 | comment | added | vonjd | Everything is fine now - thank you again! | |
| Feb 28, 2010 at 22:09 | comment | added | George Lowther | Added a couple of references. Both are only available in French though. Also, I noticed the same "unknown control sequence" problem, but it went away after refreshing the page. I see the correct formulas now both on my laptop and iphone, so it should be fine. If you're still getting the problem I'll change the notation. | |
| Feb 28, 2010 at 22:06 | history | edited | George Lowther | CC BY-SA 2.5 |
added references
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| Feb 28, 2010 at 18:46 | comment | added | vonjd | I just subscribed to your blog almostsure.wordpress.com - I was looking for something like that for a long time :-) | |
| Feb 28, 2010 at 18:33 | vote | accept | vonjd | ||
| Feb 28, 2010 at 18:32 | comment | added | vonjd | This is very, very helpful - thank you!<br> (Just one small thing: it says "Unknown control sequence '\overleftarrow'" two times in your answer - perhaps you could correct this).<br> ...And I am very much looking forward to your additional references you mention. | |
| Feb 28, 2010 at 18:19 | history | edited | George Lowther | CC BY-SA 2.5 |
added toy example
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| Feb 28, 2010 at 17:38 | history | answered | George Lowther | CC BY-SA 2.5 |