Overview
- Chapter summaries
- Detailed Illustrations
- Many worked out examples
- Numerical Solutions
- Applications to Finance
- Includes supplementary material: sn.pub/extras
Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 63)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
This book encompasses the study of hybrid switching di usion processes and their applications. The word \hybrid" signi es the coexistence of c- tinuous dynamics and discrete events, which is one of the distinct features of the processes under consideration. Much of the book is concerned with the interactions of the continuous dynamics and the discrete events. Our motivations for studying such processes originate from emerging and - isting applications in wireless communications, signal processing, queueing networks, production planning, biological systems, ecosystems, nancial engineering, and modeling, analysis, and control and optimization of lar- scale systems, under the in uence of random environments. Displaying mixture distributions, switching di usions may be described by the associated operators or by systems of stochastic di erential eq- tions together with the probability transition laws of the switching actions. We either have Markov-modulated switching di usions or processes with continuous state-dependent switching. The latter turns out to be much more challenging to deal with. Viewing the hybrid di usions as a number of di usions joined together by the switching process, they may be se- ingly not much di erent from their di usion counterpart. Nevertheless, the underlying problems become more di cult to handle, especially when the switching processes depend on continuous states. The di culty is due to the interaction of the discrete and continuous processes and the tangled and hybrid information pattern.
Similar content being viewed by others
Keywords
Table of contents (12 chapters)
-
Front Matter
-
Basic Properties, Recurrence, Ergodicity
-
Front Matter
-
-
Numerical Solutions and Approximation
-
Front Matter
-
-
Stability
-
Front Matter
-
-
Two-Time-Scale Modeling and Applications
-
Front Matter
-
-
Two-time-scale Modeling and Applications
-
Back Matter
Reviews
From the reviews:
“The book Hybrid Switching Diffusions provides a remarkable coverage of up-to-date, cutting-edge research results on switching diffusions. … As I read through the book, I was impressed by the vast number of topics covered as well as the level of technical details. … provides a thorough, up-to-date development of regime-switching diffusions. It provides a valuable reference for applied mathematicians and control scientists. The book can also be useful to researchers in other application fields who seek suitable mathematical models that may fit their own systems.” (Ruihua Liu, IEEE Control Systems Magazine, Vol. 30, October, 2010)
“This book is written for scientists, engineers, and financial analysts interested in processes described by the coexistence of discrete events and continuous dynamics. Among the topics treated are existence and uniqueness of solutions of switching diffusion equations, regularity, well posedness, recurrence, ergodicity, stability, numerical methods, and two-time-scale processes.” (IEEE Control Systems Magazine, Vol. 30, June, 2010)
Authors and Affiliations
Bibliographic Information
Book Title: Hybrid Switching Diffusions
Book Subtitle: Properties and Applications
Authors: G. George Yin, Chao Zhu
Series Title: Stochastic Modelling and Applied Probability
DOI: https://doi.org/10.1007/978-1-4419-1105-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2010
Hardcover ISBN: 978-1-4419-1104-9Published: 26 October 2009
Softcover ISBN: 978-1-4614-2470-3Published: 25 February 2012
eBook ISBN: 978-1-4419-1105-6Published: 03 October 2009
Series ISSN: 0172-4568
Series E-ISSN: 2197-439X
Edition Number: 1
Number of Pages: XVIII, 398
Topics: Probability Theory and Stochastic Processes, Operations Research/Decision Theory, Robotics and Automation, Control, Robotics, Mechatronics