Stochastic integrals with respect to consistent random measures (Q2722138)

This work is devoted to the investigation of the integral \(\int_{C}F(u)\mu(du)\), where \(C=C([0,1])\) is the space of continuous functions on \([0,1],\) \(\mu\) is a random measure on this space, \(F\) is a random map of \(C\) into itself. The random measure \(\mu\) is supposed to be adapted with the flow of \(\sigma\)-algebras generated by a Wiener process. For such measures it is turned out to define correctly well the above-mentioned integral for a wide class of random maps by finite-dimensional approximation. In this situation, Fubini's theorem is true for the adapted random maps under some auxiliary conditions.