This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models. The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book.
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... may serve as a textbook for applied scientists and engineers in stochastic approximation of complex systems. -- Zentralblatt MATH
Introductory facts related to weak convergence of the stochastic process and the convergence of semimartigales, theorems, generalizations are well organized. -- Mathematical Reviews
Introductory facts related to weak convergence of the stochastic process and the convergence of semimartigales, theorems, generalizations are well organized. -- Mathematical Reviews
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First Sentence:
The aim of this chapter is to give a brief account of basic notions on Markov and semi-Markov processes, together with martingale characterization, needed throughout this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
jump random evolution, compensating operator, stochastic additive functionals, diffusion approximation principle, phase merging principles, diffusion approximation scheme, stochastic integral functional, continuous random evolution, compact containment condition, stochastic evolutionary systems, double merging, diffusion process with generator, test functions cpe, locally independent increments, phase merging scheme, split phase space, limit diffusion process, split state space, following weak convergence, contracted operator, impulsive processes, truncated operator, independent renewal processes, limit generator, renewal moments New!
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The aim of this chapter is to give a brief account of basic notions on Markov and semi-Markov processes, together with martingale characterization, needed throughout this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
jump random evolution, compensating operator, stochastic additive functionals, diffusion approximation principle, phase merging principles, diffusion approximation scheme, stochastic integral functional, continuous random evolution, compact containment condition, stochastic evolutionary systems, double merging, diffusion process with generator, test functions cpe, locally independent increments, phase merging scheme, split phase space, limit diffusion process, split state space, following weak convergence, contracted operator, impulsive processes, truncated operator, independent renewal processes, limit generator, renewal moments New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 68
books:
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- Stochastic Processes by Ken-Iti Sato in Back Matter (1), and Back Matter (2)
- A Modern Approach to Probability Theory (Probability and its Applications) by Bert E. Fristedt in Back Matter
- Essentials of Stochastic Finance: Facts, Models, Theory by Albert N. Shiryaev in Back Matter
- Stochastic Dynamics by Hans Crauel in Back Matter
- Random Perturbation Methods by Anatoli V. Skorokhod in Back Matter
See all 68 books this book cites
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