Stochastic integration on partially ordered sets

The stochastic integral is introduced with respect to a stochastic process X = (X_s)_sεV, where V is any general partially ordered set satisfying some mild regularity conditions. As important examples the stochastic integral is constructed with respect to a class of Gaussian processes having similarities to the Brownian motion on the real line, and also with respect to L²-martingales under an assumption of conditional independence on the underlying σ-fields.