A Second Course in Stochastic Processes, Volume 2

Front Cover
Gulf Professional Publishing, May 12, 1981 - Mathematics - 542 pages
This Second Course continues the development of the theory and applications of stochastic processes as promised in the preface of
A First Course. We emphasize a careful treatment of basic structures in stochastic processes in symbiosis with the analysis of natural classes of stochastic processes arising from the biological, physical, and social sciences.
 

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Contents

CONTENTS OF A FIRST COURSE
1
Relations of Eigenvalues and Recurrence Classes
3
Special Computational Methods in Markov Chains
10
Applications to Coin Tossing
18
Index
23
Chapter 11
31
Chapter 12
72
Right Regular Sequences for the Markov Chain Sn
83
The Spectral Representation of the Transition Density
330
The Concept of Stochastic Differential Equations
340
Some Stochastic Differential Equation Models
358
A Preview of Stochastic Differential Equations
368
Elementary Problems Problems
377
Notes References
395
Chapter 16
398
An Application of Multidimensional Poisson Processes to Astronomy
404

The Discrete Renewal Theorem
93
Chapter 13
100
The Ballot Problem
107
Empirical Distribution Functions and Order Statistics
113
Some Limit Distributions for Empirical Distribution Functions
119
Chapter 14
138
Construction of a Continuous Time Markov Chain from
145
Chapter 15
157
Examples of Diffusion
169
Differential Equations Associated with Certain Functionals
191
Some Concrete Cases of the Functional Calculations
205
The Nature of Backward and Forward Equations and Calculation
213
Boundary Classification for Regular Diffusion Processes
226
Some Further Characterization of Boundary Behavior
242
Some Constructions of Boundary Behavior of Diffusion Processes
251
Conditioned Diffusion Processes
261
Some Natural Diffusion Models with Killing
272
Semigroup Formulation of Continuous Time Markov Processes
289
Further Topics in the Semigroup Theory of Markov Processes
305
Compound Poisson Processes
319
OneDimensional Geometric Population Growth
413
Deterministic Population Growth with Age Distribution
419
A Discrete Aging Model
425
FLUCTUATION THEORY OF PARTIAL SUMS OF INDEPENDENT IDENTICALLY DISTRIBUTED RANDOM VARIABLES 451
453
Some Fundamental Identities of Fluctuation Theory and Direct Applications
459
The Important Concept of Ladder Random Variables
464
Proof of the Main Fluctuation Theory Identities
468
More Applications of Fluctuation Theory Problems Notes References 459 464 468
473
QUEUEING PROCESSES 489 490 492 1 General Description 2 The Simplest Queueing Processes MM1
490
Some General OneServer Queueing Models
492
Embedded Markov Chain Method Applied to the Queueing Model MGI1
497
Exponential Service Times GM1
504
Gamma Arrival Distribution and Generalizations ExM11
506
Exponential Service with s Servers GIMs
511
The Virtual Waiting Time and the Busy Period
513
Problems
519
Notes References
525
MISCELLANEOUS PROBLEMS 527 Index
541
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About the author (1981)

Howard E. Taylor is a research chemist with the National Research Program, Water Resources Division, U.S. Geological Survey located in Boulder, Colorado. Dr. Taylor has played a major role over the past 25 years in the development of plasma spectrometric techniques in analytical chemistry, as reflected in his more than 150 technical publications and the presentation of numerous papers at national and international technical meetings. He has served as faculty affiliate at Colorado State University and has taught American Chemical Society Short Courses for more than 15 years.

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