Integral representations of random functions with values in locally convex spaces. (English. Russian original) Zbl 0835.60041

Ponomarenko, O. I.

Theory Probab. Math. Stat. 46, 129-136 (1993); translation from Teor. Jmovirn. Mat. Stat. 46, 132-141 (1992).

Summary: The author considers generalized second-order random measures \(\Phi\) with values in a locally convex space \(X\) and the operator product measures \(F\) associated with them. Stochastic integrals with respect to the measures \(\Phi\) are studied, as well as integrals of numerical functions with respect to the product measures \(F\). A generalization is given of the theorems on the integral representation of finite-dimensional random functions to generalized random functions with values in the space \(X\), and examples of such representations are considered.

MSC:

60G57	Random measures
60H05	Stochastic integrals
60G60	Random fields
60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)

Keywords:

locally convex space; harmonizing random field; correlation-homogeneous field; stochastic integrals; generalized second-order random measures