Timeline for Is this a "contradiction" on stochastic Burgers' equation? How to understand it?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Aug 3, 2019 at 17:56 | comment | added | YT_learning_math | I see, $-1/M(0)>t$ for all $t\in[0,T_{max})$ but not for $t=T_{max}$. When $t=T_{max}$, which is also a random variable, then $\mathbb{E}\int_0^{T_{max}}\beta dt'\neq\int_0^{T_{max}}\mathbb{E}\beta dt'=T_{max}$. So we can not say $T_{max}<\infty$ almost surely. | |
| Aug 3, 2019 at 17:50 | comment | added | YT_learning_math | Thanks a lot!! You make it clear. But $dM/dt=-\beta M^2$ implies $-1/M(0)>\int_0^t\beta(t') dt'$ almost surely. Taking expectation yields $-1/M(0)>\int_0^t\mathbb{E}\beta dt'=t$. What's wrong here? | |
| Aug 3, 2019 at 16:29 | history | answered | Martin Hairer | CC BY-SA 4.0 |