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2 votes
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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-...
user479223's user avatar
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3 votes
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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 ...
user479223's user avatar
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9 votes
1 answer
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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 ...
Oleg's user avatar
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