# Tag Info

### Uniqueness of solutions of Young differential equations

For such small $\beta$, we need to use Rough path theory to make sense of the integral and so below I go over that. (Indeed for $\beta\in (\frac{1}{2},1]$, there is an ODE theory for Young integrals ...
• 1,687
1 vote
Accepted

### How to rigorously prove that this sequence of stochastic processes converges to a deterministic process?

I am guessing in "The particular thing I'm trying to prove is that,..." you are talking about the convergence of discrete generator to continuous one. The natural topology for these ...
• 1,687

### Sobolev density of smooth functions which are zero on a measure zero subset

It is not always clear, what it means for a Sobolev function to vanish on a non-open subset $A\subset \Omega$. Suppose that $f\in H^s(\Omega)$, the $L^2$-bases Sobolev space of order $s\in \mathbb R$,...
• 693

### Solving (or approximating) a certain delay differential equation

Its looks like one solution to this is the function $$f(w,x) = 1+\frac{1}{2\pi i} \int_{\frac{1}{2} - i \infty}^{\frac{1}{2} + i \infty} w^{t^2} (-x)^t \Gamma(-t) dt$$ Which is obtained by applying ...
• 885
(I doubt this system in general is solvable) but a starting point is to consider $S_A = S_B = 0$ and $W_{AB}, W_{BA}$ are constant  \frac{dX_A}{dt} = -X_A(1+W_{AB}X_B^n) \\ \frac{dX_B}{dt} = -X_B(1+...