Existence and uniqueness theorem for uncertain differential equations

被引：382

作者：

Chen, X. ^{[1
]}

Liu, B. ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Uncertainty Theory Lab, Beijing 100084, Peoples R China

来源：

FUZZY OPTIMIZATION AND DECISION MAKING | 2010年 / 9卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Uncertain process; Differential equation; Existence and uniqueness theorem;

D O I：

10.1007/s10700-010-9073-2

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Canonical process is a Lipschitz continuous uncertain process with stationary and independent increments, and uncertain differential equation is a type of differential equations driven by canonical process. This paper presents some methods to solve linear uncertain differential equations, and proves an existence and uniqueness theorem of solution for uncertain differential equation under Lipschitz condition and linear growth condition.

引用

页码：69 / 81

页数：13