All Questions
Tagged with rough-paths differential-equations
3 questions
2
votes
0
answers
58
views
Does uniform convergence on compacts of drifts in rough differential equation imply convergence of solutions?
Consider the RDE
$$dY^n=b_n(Y^n) \, dt+\sigma(Y^n) \, d\mathbf X$$
where $\mathbf X$ is a rough path, $\sigma$ is as smooth as you'd like and $b_n$ are Lipschitz. If $b_n\to b$ uniformly then Friz-...
3
votes
0
answers
101
views
What is the state of the art for rough path regularity on coefficients?
Consider the rough differential equation
$$dY_t=b(Y_t,t) \, dt+\sigma(Y_t,t) \, d\mathbf X_t,$$
where $\mathbf X$ is a $p$-rough path with $1\leq p<3$. If $b$ and $\sigma$ are $C^3_b$ then we have ...
9
votes
1
answer
621
views
Uniqueness of solutions of Young differential equations
Consider the following one dimensional Young differential equation:
\begin{align*}
&Y_t=\int_0^t Y_s dX_s,\quad t\in[0,1];\\
&Y_0=0.
\end{align*}
Here the driving process $X$ is a bounded ...