5
votes
Accepted
Stochastic representation of Laplace equation with Neumann boundary condition
Yes, see Section 4.4.2 in "Stochastic Differential Equations, Backward SDEs, Partial Differential Equations" by Pardoux and Rascanu.
- 290
5
votes
Accepted
Macroscopic sets - a notion of largeness for Lebesgue null sets
By Frostman's lemma, if $E$ is a compact set of positive $\alpha$-Hausdorff content, then there exists a probability Borel measure $\mu$ supported in $E$ such that $\mu(I) \leq c |I|^\alpha $ for ...
4
votes
How far does a random walker travel before returning to the origin?
The probability $\mathbb P[\max_{t\leq \tau}|X_t|\geq a]$ is the probability to reach a point at a distance $a>0$ from the origin before returning to the origin, which is just $1/a$, see https://...
- 172k
4
votes
Understanding of rough path
You have seen all kinds of integration theories before — Itô, Stratonovich, and I'm sure plenty others. Rough paths takes a step back and asks what we want from an integration theory. And so long as ...
- 1,067
3
votes
Reflecting Brownian motion in disk
As mentioned in references here Reference for representation of heat equation with Neumann boundary condition on smooth domain using reflected Brownian motion,
you are looking for the solution of the ...
- 3,833
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