Abstract
Let X = (X t ) t∈[0,1] be a stochastic process with label Y ∈ {0, 1}.We assume that X is some Brownian diffusion when Y = 0, while X is another Brownian diffusion when Y = 1. Based on an explicit computation of the Bayes rule, we construct an empirical classification rule \(\hat g\) drawn from an i.i.d. sample of copies of (X, Y). In a nonparametric setting, we prove that \(\hat g\) is a consistent rule, and we derive its rate of convergence under mild assumptions on the model.
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Cadre, B. Supervised classification of diffusion paths. Math. Meth. Stat. 22, 213–225 (2013). https://doi.org/10.3103/S1066530713030034
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DOI: https://doi.org/10.3103/S1066530713030034