Harmonizable Stable Processes on Groups: Spectral, Ergodic and Interpolation Properties.
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PRECESSES
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This work extends to symmetric alpha-stable S alpha S processes, 1 alpha 2, which are Fourier transforms of independently scattered random measures on locally compact Abelian groups, some of the basic results known for processes with finite second moments and for Gaussian processes. Analytic conditions for subordination of left right stationarily related processes and a weak law of large numbers are obtained. The main results deal with the interpolation problem. Characterization of minimal and interpolable processes on discrete groups are derived. Also formulas for the interpolator and the corresponding interpolation error are given. This yields a solution of the interpolation problem for the considered class of stable processes in this general setting. Author
- Statistics and Probability