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0 votes

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 ...
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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 ...
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6 votes

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 $s\in \mathbb R$,...
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0 votes

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 ...
2 votes

How to analytically solve this ODEs?

(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+...
2 votes

One question about a specific first-order differential equation

There is a well-established method to obtain solutions to this equation, indeed all solutions. It is called the Fourier transform. Its application leads to an algebraic functional equation which ...
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