Stochastic Processes and their Applications
Published on 30. January 2019
255 pages
978-1-77361-580-6 (ISBN)
Description
Stochastic processes and their applications illustrates the theoretical knowledge of randomvariables along with some practical skills to analyze various stochastic dynamicalsystems in economics, engineering and other fields. It includes the most appropriateprocess for modelling in particular situations arising in economics, engineering andother fields. The book provides the readers with the insights into the development ofdifferent processes and theories like Poisson processes and the application of stochasticprocesses in biology.
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Content
- Cover
- Half Title Page
- Title Page
- Copyright Page
- About the Author
- Table of Contents
- List of Figures
- List of Tables
- Preface
- Chapter 1 Stochastic Processes, Markov Chains and Continuous-Time Applications
- 1.1. Introduction
- 1.2. Preliminary Results
- Chapter 2 Poisson Processes
- 2.1. Punctual Processes
- 2.2. Poisson Processes Definition
- 2.3. Definition Form of a Point Process
- 2.4. Properties
- 2.5. Main Results
- 2.6. Determining The Ordering
- 2.7. Alternative Definitions of Poisson Processes
- 2.8. Poisson Processes In Two or More Dimensions
- 2.9. Projections
- 2.10. Poisson Process
- 2.11. Processes Which Are Not Homogenous
- Chapter 3 Markov Chains In Continuous Time
- 3.1. Pure Markov Processes
- 3.2 Properties
- 3.3. Explosions
- 3.4 Kolmogorov Equations
- 3.5. Classification of States And Invariant Measures
- 3.6. Skeleton Process
- 3.7. Birth And Death Processes
- Chapter 4 Applications In Biology
- 4.1. Modeling The Growing Populations
- Chapter 5 Network Analysis Modeled With Stochastic Processes
- 5.1. Introduction
- 5.2. Statement of The Problem
- 5.3. Justification of Using Stochastic Processes
- 5.4. The Objectives
- 5.5. Theoretical Framework
- 5.6. Time Series Models
- 5.7. Stochastic Processes
- 5.8. Entropy as a Measure of Information
- 5.9. Markov Chains In Continuous Time: Liability of a Multiprocessor
- 5.10. Queuing
- 5.11. Queue Networks
- 5.12. Experiment Design
- 5.13. Simulation Experiment
- 5.14. Experimental Results
- 5.15. General Analysis System
- 5.16. Design of The Optimization Model
- 5.17. Optimization Model
- 5.18. Model Solution
- 5.19. Tool Design
- Chapter 6 Stochastic Modeling And Simulation
- 6.1. Counting Processes
- 6.2. Theory of Tails
- 6.3. Variations Model M/G/1
- Appendixs
- Conclusions
- Bibliography
- Index
