If I have a manifold $M$ and a chart $\left(x,U\right)$, is it possible to simulate Brownian motion on that manifold by solving an SDE in the chart representation $x\left(U\right)$ and then use the chart map $x$ to map the solution onto the manifold? Of course this would only be valid up to the time the process leaves $x\left(U\right)$.
2026-04-12 14:09:44.1776002984
Brownian motion on a manifold
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