Backward stochastic Volterra integral equations and some related problems
Backward stochastic Volterra integral equations and some related problems
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DOI：
10.1016/j.spa.2006.01.005
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发表时间：
2006-05
影响因子：
1.4
通讯作者：
J. Yong
中科院分区：
文献类型：
--
作者：
J. Yong
引入倒向随机沃尔泰拉积分方程（BSVIEs）.建立了适应解的存在性和唯一性。得到了线性BSVIEs与（前向）随机沃尔泰拉积分方程之间的对偶原理.作为对偶原理的应用，证明了BSVIEs适应解的比较定理，建立了随机积分方程最优控制的Pontryagin型最大值原理.
Backward stochastic Volterra integral equations (BSVIEs, for short) are introduced. The existence and uniqueness of adapted solutions are established. A duality principle between linear BSVIEs and (forward) stochastic Volterra integral equations is obtained. As applications of the duality principle, a comparison theorem is proved for the adapted solutions of BSVIEs, and a Pontryagin type maximum principle is established for an optimal control of stochastic integral equations.