An approximation of \(L_{p}(\Omega )\) processes. (English. Russian original) Zbl 1246.60052

Kamenshchikova, O. E.; Yanevich, T. O.

Theory Probab. Math. Stat. 83, 71-82 (2011); translation from Teor. Jmovirn. Mat. Stat. 83, 59-68 (2010).

Summary: Bounds for the increments of stochastic processes belonging to some classes of the space \( L_p(\Omega )\) are obtained in the \( L_q[a,b]\) metric. An approximation of such processes by trigonometric sums is studied in the space \( L_{q}[0,2\pi]\).

MSC:

60G07	General theory of stochastic processes
41A25	Rate of convergence, degree of approximation
42A10	Trigonometric approximation

Keywords:

the forward problem of harmonic approximation; \(L_{p}\) processes; increments; accuracy of approximation; reliability of approximation

References:

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