In Chapter 1, we will present a general introduction, survey, and background material for
stochastic differential games. A brief introduction of Linear pursuit-Evation differential
games will be given in Chapter 2 for a better understanding of the subject concepts. Chapter
3 will deal with two person Zero-sum stochastic differential games and various solution
methods. We will also introduce games with multiple modes. Formal solutions for some
classes of stochastic linear pursuit-evasion games will be given in Chapter 4. In Chapter 5,
we will discuss N-person stochastic differential games. Diffusion models are in general
not very good approximations for real world problems. In order to deal with those issues,
we will introduce weak convergence methods for two person to the stochastic differential
games in Chapter 6. In Chapter 7, will cover weak convergence methods for many player
games. In Chapter 8, we will introduce some useful numerical methods for two different
payoff structure; discounted payoff and ergodic payoff as well as the case of nonzero sum
games. We will conclude the book in Chapter 9 by giving some real world applications of
stochastic differential games to finance and competitive advertising.
We wish to express our sincere appreciation to the reviewers of the preliminary manuscript
of the book for their excellent comments and suggestions.
Dr. M. Sambandham, Professor of Mathematics, Chief Editor, International Journal of
Systems and applications.
Dr. G.R. Aryal, Assistant Professor of Statistics, Purdue University, Calumet, Indiana.
Dr. Rebecca Wooten, Assistant Professor of Mathematics & Statistics, University of South
Florida, Tampa, Florida.
Dr. V. Laksmikatham, Distinguished Professor of Mathematics, Emeritus, Florida Institute
of Technology.
Dr. Yong Xu, Assistant Professor of Mathematics at Radford University,
Dr. Kannan, Professor of Mathematics – Emeritus, University of Georgia.
Dr. Geoffrey O. Okogbaa, Professor of Industrial Engineering and Management Science,
University of South Florida, Tampa, Florida.
We would also like to thank the editorial staff of Atlantis Press, in particular, the project
manager Mr. Willie van Berkum.
Finally, a very special thanks to Beverly DeVine-Hoffmeyer for her excellent work in typing
this book.