Timeline for Sufficient conditions for a SDE to have a stationary probability measure
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Jun 10, 2022 at 0:19 | history | became hot network question | |||
| Jun 9, 2022 at 21:54 | answer | added | Julian Newman | timeline score: 4 | |
| Jun 9, 2022 at 16:38 | comment | added | Nawaf Bou-Rabee | For SDEs with multiplicative noise specifically, simple/general existence criteria are presented in Theorem 2.2.1 of link.springer.com/book/10.1007/b80743 The proof boils down to developing a Foster-Lyapunov condition with respect to a quadratic Lyapunov function $V(x) = |x|^2$. | |
| Jun 9, 2022 at 16:15 | comment | added | Nawaf Bou-Rabee | One needs the "existence of invariant measures" theorem or Krylov-Bogolyubox theorem (see Theorem 1.10 of hairer.org/notes/Convergence.pdf). In practice the assumptions of this theorem are verified by using a Foster-Lyapunov condition: see, e.g., Section 4.2 of jstor.org/stable/pdf/… | |
| Jun 9, 2022 at 15:54 | history | asked | Julian Newman | CC BY-SA 4.0 |