Stochastic systems in merging phase space

Stochastic systems in merging phase space / Vladimir S. Koroliuk, Nikolas Limnios.

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 numericall...

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Bibliographic Details
Main Author: Koroli︠u︡k, V. S. (Vladimir Semenovich), 1925-
Other Authors: Limnios, N. (Nikolaos)
Format: eBook
Language:English
Published: Singapore ; Hackensack, NJ : World Scientific, ©2005.
Subjects:
Stochastic processes.
Mathematical optimization.
MATHEMATICS > Probability & Statistics > Stochastic Processes.
Mathematical optimization
Stochastic processes
Online Access:Click for online access
Table of Contents:
  • Cover
  • Preface
  • Contents
  • 1. Markov and Semi-Markov Processes
  • 1.1 Preliminaries
  • 1.2 Markov Processes
  • 1.2.1 Markov Chains
  • 1.2.2 Continuous-Time Markov Processes
  • 1.2.3 Diffusion Processes
  • 1.2.4 Processes with Independent Increments
  • 1.2.5 Processes with Locally Independent Increments
  • 1.2.6 Martingale Characterization of Markov Processes
  • 1.3 Semi-Markov Processes
  • 1.3.1 Markov Renewal Processes
  • 1.3.2 Markov Renewal Equation and Theorem
  • 1.3.3 Auxiliary Processes
  • 1.3.4 Compensating Operators
  • 1.3.5 Martingale Characterization of Markov Renewal Processes
  • 1.4 Semimartingales
  • 1.5 Counting Markov Renewal Processes
  • 1.6 Reducible-Invertible Operators
  • 2. Stochastic Systems with Switching
  • 2.1 Introduction
  • 2.2 Stochastic Integral Functionals
  • 2.3 Increment Processes
  • 2.4 Stochastic Evolutionary Systems
  • 2.5 Markov Additive Processes
  • 2.6 Stochastic Additive Functionals
  • 2.7 Random Evolutions
  • 2.7.1 Continuous Random Evolutions
  • 2.7.2 Jump Random Evolutions
  • 2.7.3 Semi-Markov Random Evolutions
  • 2.8 Extended Compensating Operators
  • 2.9 Markov Additive Semimartingales
  • 2.9.1 Impulsive Processes
  • 2.9.2 Continuous Predictable Characteristics
  • 3. Stochastic Systems in the Series Scheme
  • 3.1 Introduction
  • 3.2 Random Evolutions in the Series Scheme
  • 3.2.1 Continuous Random Evolutions
  • 3.2.2 Jump Random Evolutions
  • 3.3 Average Approximation
  • 3.3.1 Stochastic Additive Functionals
  • 3.3.2 Increment Processes
  • 3.4 Diffusion Approximation
  • 3.4.1 Stochastic Integral Functionals
  • 3.4.2 Stochastic Additive Functionals
  • 3.4.3 Stochastic Evolutionary Systems
  • 3.4.4 Increment Processes
  • 3.5 Diffusion Approximation with Equilibrium
  • 3.5.1 Locally Independent Increment Processes
  • 3.5.2 Stochastic Additive Functionals with Equilibrium
  • 3.5.3 Stochastic Evolutionary Systems with Semi-Markov Switching
  • 4. Stochastic Systems with Split and Merging
  • 4.1 Introduction
  • 4.2 Phase Merging Scheme
  • 4.2.1 Ergodic Merging
  • 4.2.2 Merging with Absorption
  • 4.2.3 Ergodic Double Merging
  • 4.3 Average with Merging
  • 4.3.1 Ergodic Average
  • 4.3.2 Average with Absorption
  • 4.3.3 Ergodic Average with Double Merging
  • 4.3.4 Double Average with Absorption
  • 4.4 Diffusion Approximation with Split and Merging
  • 4.4.1 Ergodic Split and Merging
  • 4.4.2 Split and Merging with Absorption
  • 4.4.3 Ergodic Split and Double Merging
  • 4.4.4 Double Split and Merging
  • 4.4.5 Double Split and Double Merging
  • 4.5 Integral F'unctionals in Split Phase Space
  • 4.5.1 Ergodic Split
  • 4.5.2 Double Split and Merging
  • 4.5.3 Triple Split and Merging
  • 5. Phase Merging Principles
  • 5.1 Introduction
  • 5.2 Perturbation of Reducible-Invertible Operators
  • 5.2.1 Preliminaries
  • 5.2.2 Solution of Singular Perturbation Problems
  • 5.3 Average Merging Principle
  • 5.3.1 Stochastic Evolutionary Systems
  • 5.3.2 Stochastic Additive F'unctionals
  • 5.3.3 Increment Processes
  • 5.3.4 Continuous Random Evolutions
  • 5.3.5 Jump Random Evolutions
  • 5.3.6 Random Evolutions with Markov Switching
  • 5.4 Diffusion Approximation Principle
  • 5.4.1 Stochastic Integral F'unctionals
  • 5.4.2 Continuous Random Evolutions
  • 5.4.3 Jump Random Evolution.

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