CANONICAL PROPERTY OF REPRESENTATIONS OF GAUSSIAN PROCESSES WITH SINGULAR VOLTERRA KERNELS

We consider the Gaussian process X_λ defined by parameterizing a singular kernel of Volterra-type introduced in Ref. 1. The kernel has a close connection with the noncanonical representation. The result is that the representation is canonical (resp. noncanonical) if λ < 1/2 (resp. λ > 1/2), being independent of the choice of g of a class of functions (Theorem 3).