Supervised classification of diffusion paths
Benoı̂t Cadre · Mathematical Methods of Statistics · 2013
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.