Questions tagged [rough-path-theory]

The rough paths theory gives an almost deterministic purpose of perspective around integrale stochastic, as opposed to the semi-martingale approach, which is highly probabilistic generally. The rough paths theory is a powerful method that allows one to define noisy systems in a wide variety of situations (well beyond the Brownian motion case).

The rough paths theory gives an almost deterministic purpose of perspective around integrale stochastic, as opposed to the semi-martingale approach, which is highly probabilistic generally. The rough paths theory is a powerful method that allows one to define noisy systems in a wide variety of situations (well beyond the Brownian motion case).

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Signature of a path under linear transformation

Let $x$ be a $\mathbb{R}^n$ valued path with finite variation on $[0,T]$ and $A$ be a matrix of $d\times n$. It is easy to see that $Ax$ is a path with finite variation. Let $S^N(x)_{0,1}$ be the step-N signature of $x$ on $[0,1]$. What is the…
George
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Prerequisite of rough path theory

I'm currently reading A Course on Rough Paths: With an Introduction to Regularity Structures, but I find it difficult to start on even though I've taken undergraduate mathematical analysis, linear algebra, algebra, ODE and PDE courses of the math…