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Approximation of a Random Process with Variable Smoothness by Hashorva, Enkelejd; Lifshits, Mikhail; Seleznjev, Oleg is a scholarly article available to read on EtoBox.

What is Approximation of a Random Process with Variable Smoothness about?

We consider the rate of piecewise constant approximation to a locally stationary process $X(t),t\in [0,1]$, having a variable smoothness index $\alpha(t)$. Assuming that $\alpha(\cdot)$ attains its unique minimum at zero and satisfies the regularity condition, we propose a method for construction of observation points (composite dilated design) and find an asymptotics for the integrated mean square error, where a piecewise constant approximation $X_n$ is based on $N(n)\sim n$ observations of $X$. Further, we prove that the suggested approximation rate is optimal, and then show how to find an optimal constant.

Author

Hashorva, Enkelejd; Lifshits, Mikhail; Seleznjev, Oleg

Published

2012

Language

EN