The absolute continuity of random measures generated by symmetric stochastic integrals. (English. Ukrainian original) Zbl 0998.60048

Radchenko, V. M.

Theory Probab. Math. Stat. 64, 161-165 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 136-140 (2001).

This article is a further extension of the author’s previous article [Ukr. Math. J. 51, No. 8, 1226-1236 (1999); translation from Ukr. Mat. Zh. 51, No. 8, 1087-1095 (1999; Zbl 0957.60054)]. The author proposes sufficient conditions for integrability of the function \(g=h(f)\) with respect to a general random measure \(\mu\), when \(h\) is an analytic function and \(f\) is integrable with respect to \(\mu\). Results on absolute continuity of \(\int_A h(f) d\mu\) are presented.

Reviewer: N.M.Zinchenko (Kyïv)

MSC:

60G57

Random measures

Keywords:

random measure; integrability; absolute continuity

Citations:

Zbl 0957.60054