Empirical risk minimization algorithm for multiclass classification of S.D.E. paths

Functional data analysis (Ramsay & Silverman, 2005) is an active field of research, as technological progress has facilitated the large-scale collection of such data in a wide range of fields, including biology (Crow, 2017)), physics (Romanczuk et al., 2012)), and finance (Lamberton & Lapeyre, 2011)). In particular, the classification of functional data is at the core of recent research efforts (Ismail Fawaz et al., 2019; Xiao et al., 2022). A specific case arises when the data are assumed to be generated by diffusion processes. The literature on statistical methods for stochastic differential equations has generated significant attention.