"The academic level of this book is not too elementary yet not too advanced. It is assumed that the reader has taken calculus-based probability theory and statistics. Not a whole lot of statistical analysis is present in this book. In applications there are some attempts to estimate parameters of stochastic processes via linear regression, maximum likelihood and method of moments estimators. Typically, a course on stochastic processes is taught to pure mathematics, applied mathematics, physics, and engineering majors, and the selection of processes and level of exposition differ. Most of the books involved sigma algebra, martingales, and Ito calculus, which I deliberately not mention in my book. My book is written for statistics majors who benefit from seeing less theory but more simulated trajectories and serious applications, possibly with data analysis involved"--
Stochastic Processes with R: An Introduction cuts through the heavy theory that is present in most courses on random processes and serves as practical guide to simulated trajectories and real-life applications for stochastic processes.
Arvustused
CRC Press Title: Stochastic Processes with R ISBN: 9781032153735 was successfully transmitted to the Library of Congress. "This book is useful for simulating Markov chains, Poisson processes, and Brownian motion. The book can be used as supplementary reading for a first course in stochastic processes at the undergraduate-graduate level."
- David J. Olive, Technometrics, November 2022.
Preface |
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vii | |
Author |
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ix | |
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1 Stochastic Process, Discrete-time Markov Chain |
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1 | (42) |
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1.1 Definition of Stochastic Process |
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1 | (1) |
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1.2 Discrete-time Markov Chain |
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1 | (2) |
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1.3 Chapman-Kolmogorov Equations |
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3 | (2) |
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1.4 Classification of States |
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5 | (2) |
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1.5 Limiting Probabilities |
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7 | (2) |
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9 | (5) |
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14 | (14) |
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1.8 Applications of Markov Chain |
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28 | (9) |
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37 | (6) |
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43 | (18) |
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2.1 Definition of Random Walk |
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43 | (2) |
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2.2 Must-Know. Facts About Random Walk |
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45 | (2) |
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47 | (4) |
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2.4 Applications of Random Walk |
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51 | (6) |
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57 | (4) |
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61 | (20) |
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3.1 Definition and Must-Know Facts About Poisson Process |
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61 | (5) |
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66 | (4) |
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3.3 Applications of Poisson Process |
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70 | (6) |
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76 | (5) |
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4 Nonhomogeneous Poisson Process |
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81 | (24) |
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4.1 Definition of Nonhomogeneous Poisson Process |
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81 | (3) |
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84 | (7) |
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4.3 Applications of Nonhomogeneous Poisson Process |
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91 | (11) |
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102 | (3) |
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5 Compound Poisson Process |
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105 | (12) |
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5.1 Definition of Compound Poisson Process |
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105 | (2) |
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107 | (4) |
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5.3 Applications of Compound Poisson Process |
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111 | (2) |
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113 | (4) |
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6 Conditional Poisson Process |
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117 | (12) |
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6.1 Definition of Conditional Poisson Process |
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117 | (2) |
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119 | (4) |
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6.3 Applications of Conditional Poisson Process |
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123 | (2) |
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125 | (4) |
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7 Birth-and-Death Process |
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129 | (12) |
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7.1 Definition of Birth-and-Death Process |
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129 | (3) |
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132 | (3) |
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7.3 Applications of Birth-and-Death Process |
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135 | (2) |
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137 | (4) |
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141 | (12) |
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8.1 Definition of Branching Process |
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141 | (4) |
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145 | (3) |
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8.3 Applications of Branching Process |
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148 | (1) |
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149 | (4) |
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153 | (30) |
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9.1 Definition of Brownian Motion |
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153 | (3) |
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9.2 Processes Derived from Brownian Motion |
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156 | (3) |
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156 | (1) |
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9.2.2 Brownian Motion with Drift and Volatility |
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157 | (1) |
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9.2.3 Geometric Brownian Motion |
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157 | (1) |
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9.2.4 The Ornstein-Uhlenbeck Process |
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158 | (1) |
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159 | (8) |
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9.4 Applications of Brownian Motion |
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167 | (10) |
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177 | (6) |
Recommended Books |
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183 | (2) |
List of Notations |
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185 | (2) |
Index |
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187 | |
Olga Korosteleva, PhD, is a professor of statistics in the Department of Mathematics and Statistics at California State University, Long Beach (CSULB). She earned her Bachelors degree in mathematics in 1996 from Wayne State University in Detroit, and her PhD in statistics from Purdue University in West Lafayette, Indiana, in 2002. Since then she has been teaching statistics and mathematics courses at CSULB.