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.

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://...

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 ...

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 ...

Only top scored, non community-wiki answers of a minimum length are eligible

#### Related Tags

stochastic-processes × 2296pr.probability × 1504

stochastic-calculus × 643

stochastic-differential-equations × 369

brownian-motion × 206

reference-request × 196

probability-distributions × 187

markov-chains × 183

martingales × 149

measure-theory × 144

fa.functional-analysis × 142

st.statistics × 139

random-walks × 118

ap.analysis-of-pdes × 52

real-analysis × 51

ergodic-theory × 43

limits-and-convergence × 42

gaussian × 41

ds.dynamical-systems × 38

oc.optimization-and-control × 37

measure-concentration × 36

levy-processes × 34

co.combinatorics × 33

semigroups-of-operators × 30

differential-equations × 25