Stochastic operator integrals
The authors suggest a construction of an operator stochastic integral of the type \(\int^{\tau}_{0}A(t)dE(t)\), \(\tau\in (0,\infty)\), where \(A(t),\) \(t\in (0,\infty)\), is a family of commuting normal operators in a given separable Hilbert space H and \(E(\Delta),\Delta\in {\mathcal B}(0,\infty)\), is the decomposition of the unit operator in H. Several properties of this integral are established. Let us note that the operator stochastic integral treated here could be considered as a generalization of the well-known stochastic integrals with respect to square integrable martingales.
scientific article; zbMATH DE number 4034788