Best approximation for classes of random processes
Alexander Buslaev and Oleg Seleznjev
Department of Mathematical Statistics,
Lund Institute of Technology,
We consider the best approximation order for classes of random processes.
The close relationship between the smoothness properties of a function and
the best rate of its linear approximation is one of the basic ideas of
conventional (deterministic) approximation theory. We investigate similar
properties for random functions. Hölder's class of random processes
is studied in more detail. Several types of extremal characteristics of an
approximation accuracy are proposed. For Hölder's class of random processes,
the exact order of these characteristics are found in different metrics.
These results can be used, for example, for a justification of a specific
approximation method selection in approximation problems.
approximation, random process, Gaussian process, Kahrunen-Loève expansion,