Timeline for Stochastic integral with respect to a random field
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 11, 2020 at 23:48 | comment | added | Heisenberg | Maybe @MartinHairer can correct me but I think if we were to think of a Hilbert space valued Weiner process, $Qf(\cdot)=\int c(s,\cdot) f(s)ds$, $f\in H$ and $Q\in L(H).$ | |
| Jul 11, 2020 at 18:35 | comment | added | user81883 | @MartinHairer Usually there is some linear operator $Q$ with finite trace in $C(\mathbb{R})$ so that $W_t-W_s\sim N(0,(t-s)Q)$. What is $Q$ in terms of $c$? | |
| Jul 8, 2020 at 1:15 | history | bounty ended | Heisenberg | ||
| Jul 7, 2020 at 19:43 | comment | added | Martin Hairer | Edited for clarity. | |
| Jul 7, 2020 at 19:42 | history | edited | Martin Hairer | CC BY-SA 4.0 |
Edited for clarity.
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| Jul 7, 2020 at 19:22 | vote | accept | Heisenberg | ||
| Jul 7, 2020 at 19:22 | comment | added | Heisenberg | Thank you this helps a lot. This is probably a very basic questions but I don't fully understand how you interpret $c$. On the left side of the second equation you have $c$ evaluated at two measures and on the right side $c$ is evaluated at to real numbers. Why is this possible? | |
| Jul 6, 2020 at 11:02 | history | answered | Martin Hairer | CC BY-SA 4.0 |