具随机生成元的受控随机发展方程的Pontryagin型最大值原理（英文）  

Pontryagin-type stochastic maximum principle of stochastic evolution equation with a random generator

作　　者：张宇 ZHANG Yu(School of Mathematics, Sichuan University, Chengdu 610064, China)

机构地区：[1]四川大学数学学院

出　　处：《四川大学学报（自然科学版）》2019年第3期377-386,共10页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11471231,11231007)

摘　　要：本文研究了当控制区域是凸集时带有随机生成元的受控正向随机发展方程的Pontryagin型最大值原理.运用Malliavin分析方法,本文给出了当p≥2时控制系统温和解的存在唯一性,运用转置方法获得了当1<q≤2时对偶系统的适定性,并运用凸变分方法推导了相应的最大值原理.In this paper, we establish a Pontryagin-type maximum principle for a control stochastic evolution equation with a random generator and a convex control domain. Given p≥2, the existence and uniqueness of mild solution to the control system are obtained by using the Malliavin calculus. To study the well-posedness of the adjoint system when 1 <q≤2,the transposition method is used.The well-posedness results for these systems are established.The desired Pontryagin-type maximum principle is deduced by a standard convex perturbation technique.

关 键 词：随机发展方程 随机生成元 最大值原理 

分 类 号：O231.4[理学—运筹学与控制论]