Mean-square integral and differential of fuzzy stochastic processes (Q1303934)

Fuzzy stochastic processes (fsp) are families \(\{X(t)\}\) of fuzzy random variables \(X(t)\) in the sense of Puri and Ralescu. If \(X_\alpha(t)\) is the \(\alpha\)-cut of \(X(t)\) and \(d(\cdot,\cdot)\) the Hausdorff-distance, the author uses the metric \(\rho(X(t),Y(t))= \left[ E\left(\sup_{\alpha\in [0,1]} d(X_\alpha(t), Y_\alpha(t))\right)^2\right]^{1/2}\) to define mean-square (ms) integration and ms differentiation of fsp's. He proves properties of this ms-calculus which follow broadly steps used in considering calculus of classical functions. Gaussian fuzzy stochastic processes are also discussed.