Chaos
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Space derivative of Brownian local time
@MateuszKwaśnicki thanks! I've done some calculations and apparently the derivative of the Local time is actually in $S_{-p}$ for $p>17/24$ while the dirac's delta is in $S_{-p}$ for $p>5/12$, so it's even "worst" than the derivative of the wiener process
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Space derivative of Brownian local time
@MateuszKwaśnicki Well, I was hoping that the derivative was actually a function
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Space derivative of Brownian local time
Thanks! @MartinHairer Do you mean the Ray–Knight theorem? How can I use it could you mind giving me some hint?
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Continuity of translation operator in fractional white noise analysis
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Feynman Kac representation for nonlinear heat equation
@DanieleTampieri Ciao Daniele! I have Freidlin's book but I wasn't able to find a Feynman Kac representation for an equation in which the source was actually nonlinear! The linear case although it could have relevance from a PDE perspective, is not interesting for my purposes
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Feynman Kac representation for nonlinear heat equation
@CarloBeenakker my main question was regarding the existence of a Feynman Kac representation, in addition I was asking for a confirmation on whether such an expression is actually correct.
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Feynman Kac representation for nonlinear heat equation
@CarloBeenakker indeed, this is just another way to write down the equation, but in my case (there's a lot of context i didn't introduced in the question) this way of writing things down can be useful
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Existence of a solution for this hypoelliptic-alike PDE
Thank you so much for taking the time to look for the bibliography Daniele! One of the main issues is that in general in the text you mentioned the authors consider the state variable over a bounded domain, in my case the X's live in $\mathbb R^d$. Still the book was quite useful! Buona Pasqua anche a te!
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Existence of a solution for this hypoelliptic-alike PDE
Thanks Daniele for all this insights, tomorrow I'll read your explanation in detail and for sure I'll check out the references you provided. Grazie mille e saluti da un compaesano
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Existence of a solution for this hypoelliptic-alike PDE
I've thought of that (actually since I am working with stochastic analysis I've thought of applying the S-transform) to obtain something like what you said. The problem is I don't know whether I can apply the inverse of the transformation and obtain a solution to the original equation. Is the solution invariant under the transformation?