Outer measures and stochastic integrals (Q811674)

A general method, in the context of group valued measures, for constructing a countably additive function on a \(\sigma\)-field from a primitive function defined only on a pre-ring is exploited to generate both stochastic measures (i.e., additive processes indexed by sets) and stochastic integrals of (not necessarily adapted) stochastic processes. The usual Itô integral of a predictable process is only one of the special cases of this approach. A key role is played by the notions of quasi-additivity, quasi-summability and quasi-bounded variation introduced in this paper to extend classical results to more general settings.