Statistical Estimation for a Class of Self-Regulating Processes

摘要

Self-regulating processes are stochastic processes whose local regularity, as measured by the pointwise Holder exponent, is a function of amplitude. They seem to provide relevant models for various signals arising for example in geophysics or biomedicine. We propose in this work an estimator of the self-regulating function (that is, the function relating amplitude and Holder regularity) of the self-regulating midpoint displacement process and study some of its properties. We prove that it is almost surely convergent and obtain a central limit theorem. Numerical simulations show that the estimator behaves well in practice.