Approximation of integrals with respect to a random measure by integrals with respect to a real measure. (English. Ukrainian original) Zbl 0923.60053

Radchenko, V. M.

Theory Probab. Math. Stat. 55, 177-179 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 165-166 (1996).

The author shows that an integral \(\int f d\mu\) with respect to a random measure \(\mu\) may be approximated (in probability as \(n\to\infty\)) by integrals \(\int f d\mu_n\), where the random measures \(\mu_n\) are determined by values of the measure \(\mu\) on the finite number of sets which do not depend on \(f\) and by some nonrandom measure.

Reviewer: M.P.Moklyachuk (Kyïv)

MSC:

60G57

Random measures

Keywords:

random measure; integral with respect to random measure; approximation