We know (see here ) that the random walk generated in $R^1$ can converge in distribution to the standard Brownian motion $B_t$ in $R^1$. Could anybody provide a rigorous mathematical proof, how a random walk generated in $R^3$ can converge in distribution to the standard Brownian motion on a sphere $S^2$ using an appropriate mapping?
2026-03-30 01:47:53.1774835273
Convergence of the random walk to the Brownian motion on $S^2$
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