Newton-Leibniz formula of set-valued stochastic processes
Liu Chang-yu, LI Shi-kai, Pla Uni · Journal of PLA University of Science and Technology · 2005
In order to study the derivative and integral theories of the set-valued stochastic processes, an introduction is firstly made of the concepts of the strong (weak) mean square integral and derivative of the bounded closed convex set-valued stochastic processes. Then the relations between the mean square derivative and the mean square integral were discussed by means of support functions and Hausdorff measure. Based on them, the Newton-Leibniz formulas of the mean square integral of the bounded closed convex set-valued stochastic processes were proved. Fimally an example was presented. The conclusions are important to the further studying of the set-valued stochastic derivative equations.