A linear prediction problem for symmetric \(\alpha\)-stable processes with \(<\alpha <1\) (Q1089994)

A linear prediction problem for symmetric \(\alpha\)-stable processes, \(<\alpha <1\), which admit prediction in the \textit{K. Urbanik} sense [Proc. Fifth Berkeley Symp. Math. Stat. Probab., Univ. Calif. 1965/66, 2, Part 1, 235-258 (1967; Zbl 0226.60065)] is studied. The author proves a canonical representation theorem for the completely nondeterministic part of the process. This result is parallel to Urbanik's theorem, which for the class of symmetric stable processes includes the case \(1<\alpha <2.\) In this paper, the author considers a class of processes which have infinite first moment. The restriction \(\alpha >\) depends on the author's sufficient condition for integrability of functions with values in the Fréchet-space \(L^{\alpha}\).