Uncertain Differential Equations - Yao, Kai.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2016)
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
Introduction -- Uncertain Variable -- Uncertain Process -- Contour Process -- Uncertain Calculus -- Uncertain Differential Equation -- Uncertain Calculus with Renewal Process -- Uncertain Differential Equation with Jumps -- Multi-Dimensional Uncertain Differential Equation -- High-Order Uncertain Differential Equation.
Keywords: Computational intelligence; Social sciences -- Mathematics; Computer science -- Mathematics; Mathematical statistics; Computational Intelligence; Mathematics in Business, Economics and Finance; Probability and Statistics in Computer Science