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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.
List of contents
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.
Summary
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.
Additional text
“The book under review is the first textbook on this topic. … The book is well organized and endowed with many illustrative examples. It is suitable for mathematicians interested in the finance theory.” (Andrzej Nowak, zbMATH 1378.60009, 2018)
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"The book under review is the first textbook on this topic. ... The book is well organized and endowed with many illustrative examples. It is suitable for mathematicians interested in the finance theory." (Andrzej Nowak, zbMATH 1378.60009, 2018)
