An Alternative Construction of the Strong Embedding for the Simple Random Walk
نویسنده
چکیده
We give a new proof of the Komlós-Major-Tusnády embedding theorem for the simple random walk. The only external tool that we use is the Schauder-Tychonoff fixed point theorem for locally convex spaces. Besides that, the proof is almost entirely based on a series of soft arguments and easy inequalities, and no hard computations (implicit or explicit) are involved. This provides the first genuine alternative to the quantile transform and the Hungarian construction.
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