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Abstract: We discuss the distributions of three functionals of the free Brownian bridge: its $\L^2$-norm, the second component of its signature and its L\'evy area. All of these are freely infinitely ...
One more approach to the convergence of the empirical process to the Brownian bridge
Empirical process Donsker Theorem Brownian bridge
2009/9/16
A theorem of Donsker asserts that the empirical process converges in distribution to the Brownian bridge. The aim of this paper is to provide a new and simple proof of this fact.