Timeline for Solutions to linear SDE with many noise sources
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2017 at 3:07 | comment | added | JGWang | @tobias Yes, you are right, if the components of $W$ are independent, then we have $\sum_{i,j}a_{ij}=\sum_{i}a_{ii}$. | |
| Mar 31, 2017 at 6:20 | comment | added | tobias | I mean that if the $W^{(i)}$ are independent then we have $\sum_{i,j} a_{ij} = \sum_i a_{ii}$ in the sums from above. Would you agree? | |
| Mar 31, 2017 at 1:46 | comment | added | JGWang | @tobias $\sum\limits_{i,j=1}^na_{ij}=\sum\limits_{i=1}^n\sum\limits_{j=1}^na_{ij}$. What "simplify" do you want? | |
| Mar 30, 2017 at 13:00 | comment | added | tobias | But doesn't that mean that we can simplify the sum terms that range over both i and j? | |
| Mar 30, 2017 at 12:49 | vote | accept | tobias | ||
| Mar 30, 2017 at 7:21 | comment | added | JGWang | @tobias If the components of W are independent (or orthogonal in local martingale), then $\langle W^{(i)},W^{(j)}\rangle =0, i\ne j$. | |
| Mar 30, 2017 at 7:14 | history | edited | JGWang | CC BY-SA 3.0 |
edited body
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| Mar 30, 2017 at 7:13 | comment | added | tobias | Well, yes I am quite new to the field, so I am cautious when it comes to simplify the formula. But, again, isn't it possible to simplify the formulas dramatically because of what I said beforehand? | |
| Mar 30, 2017 at 7:10 | comment | added | JGWang | @tobias Thank you again for your help to improve the formulating. If it is not clear please let me know, I will do my best to improve it. | |
| Mar 30, 2017 at 7:07 | comment | added | tobias | You are doing a great job! But with the current definition of \sigma_{ij} couldn't we dramatically simplify the solution by considerung in the sums ranging over i and j simultaneaously only those terms with i=j? | |
| Mar 30, 2017 at 7:02 | history | edited | JGWang | CC BY-SA 3.0 |
improve formatting
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| Mar 30, 2017 at 6:41 | comment | added | tobias | Okay, that looks much better. Could you write down a bit more on \sigma_{ij} then as well? That would be great! Many thanks in advance! | |
| Mar 30, 2017 at 3:09 | comment | added | JGWang | @tobias Thank you for your replication. I already add the definition of W, <W,W>, and <H,Y>. | |
| Mar 30, 2017 at 3:05 | history | edited | JGWang | CC BY-SA 3.0 |
give the definitions of W and <W,W>
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| Mar 29, 2017 at 13:31 | comment | added | tobias | Also, when n=1, do the equations come down to the ones like in math.stackexchange.com/questions/1788853/… or en.wikipedia.org/wiki/… ? | |
| Mar 29, 2017 at 12:31 | comment | added | tobias | Many thanks for your input! Could you tell me what the scalar (like d<H,Y>) is supposed to mean? | |
| Mar 29, 2017 at 8:02 | history | answered | JGWang | CC BY-SA 3.0 |