TY - BOOK ID - 8283967 TI - Hybrid switching diffusions : properties and applications AU - Yin, George AU - Zhu, Chao PY - 2010 SN - 1441911049 9786612835131 1441911057 1282835130 PB - New York : Springer, DB - UniCat KW - Hybrid systems. KW - Mathematics. KW - Stochastic processes -- Mathematical models. KW - Stochastic processes KW - Hybrid systems KW - Mathematical Statistics KW - Mathematics KW - Physical Sciences & Mathematics KW - Mathematical models KW - Diffusion processes. KW - Stochastic differential equations. KW - Switching theory. KW - Operations research. KW - Decision making. KW - Probabilities. KW - Control engineering. KW - Robotics. KW - Mechatronics. KW - Automation. KW - Probability Theory and Stochastic Processes. KW - Operation Research/Decision Theory. KW - Robotics and Automation. KW - Control, Robotics, Mechatronics. KW - Automatic control KW - Digital electronics KW - Electric networks KW - Electric switchgear KW - Information theory KW - Logic, Symbolic and mathematical KW - Machine theory KW - Mathematical physics KW - System analysis KW - Telecommunication KW - Differential equations KW - Fokker-Planck equation KW - Markov processes KW - Distribution (Probability theory. KW - Operations Research/Decision Theory. KW - Operational analysis KW - Operational research KW - Industrial engineering KW - Management science KW - Research KW - System theory KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Mechanical engineering KW - Microelectronics KW - Microelectromechanical systems KW - Control engineering KW - Control equipment KW - Control theory KW - Engineering instruments KW - Automation KW - Programmable controllers KW - Automatic factories KW - Automatic production KW - Computer control KW - Engineering cybernetics KW - Factories KW - Mechanization KW - Assembly-line methods KW - Automatic machinery KW - CAD/CAM systems KW - Robotics KW - Deciding KW - Decision (Psychology) KW - Decision analysis KW - Decision processes KW - Making decisions KW - Management KW - Management decisions KW - Choice (Psychology) KW - Problem solving KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Decision making UR - https://www.unicat.be/uniCat?func=search&query=sysid:8283967 AB - This book presents a comprehensive study of hybrid switching diffusion processes and their applications. The motivations for studying such processes originate from emerging and existing applications in wireless communications, signal processing, queueing networks, production planning, biological systems, ecosystems, financial engineering, and modeling, analysis, and control and optimization of large-scale systems, under the influence of random environment. One of the distinct features of the processes under consideration is the coexistence of continuous dynamics and discrete events. This book is written for applied mathematicians, applied probabilists, systems engineers, control scientists, operations researchers, and financial analysts. Selected materials from the book may also be used in a graduate level course on stochastic processes and applications or a course on hybrid systems. A large part of the book is concerned with the discrete event process depending on the continuous dynamics. In addition to the existence and uniqueness of solutions of switching diffusion equations, regularity, Feller and strong Feller properties, continuous and smooth dependence on initial data, recurrence, ergodicity, invariant measures, and stability are dealt with. Numerical methods for solutions of switching diffusions are developed; algorithms for approximation to invariant measures are investigated. Two-time-scale models are also examined. The results presented in the book are useful to researchers and practitioners who need to use stochastic models to deal with hybrid stochastic systems, and to treat real-world problems when continuous dynamics and discrete events are intertwined, in which the traditional approach using stochastic differential equations alone is no longer adequate. ER -