集值随机过程的Newton-Leibniz公式

为了研究集值随机过程的微积分理论，首先介绍了有界闭凸集值随机过程强(弱)均方积分、强(弱)均方导数的定义，然后利用支撑函数与Hausdorff度量的性质，讨论了均方可导与均方可积之间的关系；以此为基础，分别证明了集值随机过程强、弱均方积分的Newton—Leibniz公式。最后给出了集值随机过程Newton-Leibniz公式的应用实例，为进一步研究集值随机微分方程奠定了良好的理论基础。

Newton -Leibniz formula of set -valued stochastic processes

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.