Timeline for Ornstein Uhlenbeck process with discontinuous drift
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 23 at 12:12 | vote | accept | painday | ||
| May 23 at 10:38 | answer | added | Kostya_I | timeline score: 1 | |
| May 22 at 17:08 | comment | added | painday | @Kostya_l Since the process in the question has singular(discontinuous)drift, I think this process may not have nice enough ergodic properties(uniqueness of invariant measure and convergence to a unique stationary measure regardless of initial distribution, etc.) In statistical physics nonergodic processes can lead to fascinating phase transition phenomena, which is also a motivation of this question. | |
| May 22 at 16:41 | comment | added | Kostya_I | But then, one shouldn't expect the limit in the left-hand side to depend on $\mathbf{X}$ at all, since the process converges to its stationary distribution at large $t$. | |
| May 22 at 13:17 | history | edited | painday | CC BY-SA 4.0 |
correct typos
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| May 22 at 13:11 | history | edited | painday | CC BY-SA 4.0 |
correct typos
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| May 22 at 13:07 | comment | added | painday | $\mathbb E^{\mathbf X}\{f(\mathbf X)\}$ means the mathematical expectation of $f(\mathbf X)$ given initial value $X_{t=0}=\mathbf X.$ Thanks for pointing this out and I'll add it in the question @Kostya_I | |
| May 22 at 8:25 | comment | added | Kostya_I | What is $\mathbb{E}^{\mathbf{X}}$, and what is $\mathbf{X}$ in your last equation? | |
| May 22 at 5:31 | history | edited | painday | CC BY-SA 4.0 |
add missing description
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| May 22 at 5:11 | history | asked | painday | CC BY-SA 4.0 |