Stochastic integration for set-indexed processes

In this paper, we are concerned with the construction of a stochastic integral, when the integrator is a set-indexed stochastic process. For this purpose, we adopt Blei’s point of view and we get this integral by means of the bimeasure he introduced. This enables us to enlarge the class of integrators. Here, the integral is first defined for point-indexed integrands and later for set-indexed ones. Then we generalize this definition to local processes.