Chapter 10 ALGEBRAIC METHODS IN MARKOV CHAINS
1.Preliminaria
2.Relations of Eigenvalues and Recurrence Claum
3.Periodic Classes
4.Special Computational Methods in Markov Chains
5.Examples
6.Applications to Coin Tomin
Elementary Problems
Problermt
Nores
References
Chapter 11 RATIO THEoREMS oF TRANSITl0N PROBABILITIES AND APPLICATl0NS
1.Taboo Probabilities
2.RatioTheorems
3.Existence of Generalized Stationary Distributions
4.Interpretation of Generalized Stationary Distributions
5.Regular， Superregular， and Subregular Sequences for Markov Chains
6.Stopping Rule Problems
Elementary Problems
Problems
Notes
References
Chapter 12 SUMS OF INDEPENDENT RANDOM VARIABLES AS A MARKOV CHAIN
1.Recurrence Properties of Sums of Independent Random Variables
2.Local Limit Theorems
3.Right Regular Sequences for the Markov Chain
4.The Discrete Renewal Theorem
Elementary Problems
Problems
Notes
References
Chapter 13 ORDER STATISTICS， POISSON PROCESSES， AND
APPLICATIONS
1.Order Statistics and Their Relation to Poisson Processes
2.The Ballot Problem
3.Empirical Distribution Functions
4.Some Limit Distributions for Empirical Distribution Functions
Elementary Problems
Problems
Notes
References
Chapter 14 CONTINUOUS TIME MARKOV CHAINS
1. Differentiability Properties of Transition Probabilities
2. Conservative Processes and the Forward and Backward Differential Equations
3. Construction of a Continuous Time Markov Chain from Its Infinitesimal Parameters
4. Strong Markov Property
Problems
Notes
References
Chapter 15 DIFFUSION PROCESSES ..
1. General Description
2. Examples of Diffusion
3. Differential Equations Associated with Certain Functionals
4. Some Concrete Cases of the Functional Calculations
5. The Nature of Backward and Forward Equations and Calculation of Stationary Measures
6. Boundary Classification for Regular Diffusion Processes
7. Some Further Characterization of Boundary Behavior
8. Some Constructions of Boundary Behavior of Diffusion Processes
9. Conditioned Diffusion Processes
10. Some Natural Diffusion Models with Killing
11. Semigroup Formulation of Continuous Time Markov Processes
12. Further Topics in the Semigroup Theory of Markov Processes and Applications to Diffusions
13. The Spectral Representation of the Transition Density for a Diffusion
14. The Concept of Stochastic Differential Equations
15. Some Stochastic Differential Equation Models
16. A Preview of Stochastic Differential Equations and Stochastic Integrals
Elementary Problems
Problems
Notes
References
Chapter 16 COMPOUNDING STOCHASTIC PROCESSES
1. Multidimensional Homogeneous Poisson Processes
2. An Application of Multidimensional Poisson Processes to Astronomy
3. Immigration and Population Growth
4. Stochastic Models of Mutation and Growth
5. One-Dimensional Geometric Population Growth
6. Stochastic Population Growth Model in Space and Time
7. Deterministic Population Growth with Age Distribution
8. A Discrete Aging Model
9. Compound Poisson Processes
Elementary Problems
Problems
Notes
References
Chapter 17 FLUCTUATION THEORY OF PARTIAL SUMS OF INDEPENDENT IDENTICALLY DISTRIBUTED RANDOM VARIABLES
1. The Stochastic Process of Partial Sums
2. An Equivalence Principle
3. Some Fundamental Identities of Fluctuation Theory and Direct Applications
4. The Important Concept of Ladder Random Variables
5. Proof of the Main Fluctuation Theory Identities
6. More Applications of Fluctuation Theory
Problems
Notes
References
Chapter 18 QUEUEING PROCESSES
1. General Description
2. The Simplest Queueing Processes(M/M/l)
3. Some General One-Server Queueing Models
4. Embedded Markov Chain Method Applied to the Queueing Model(M/GI/l)
5. Exponential Service Times(G/M/1)
6. Gamma Amval Dtstnbutlon and Generalizations(Ek/M/1)
7. Exponential Service with s Servers(GI/M/s)
8. The Virtual Waiting Time and the Busy Period
Problems
Notes
References
MISCELLANEOUS PROBLEMS
Index
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