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Stochastic Processes with R: An Introduction [Kõva köide]

(California State University, Long Beach, USA)
  • Formaat: Hardback, 190 pages, kõrgus x laius: 234x156 mm, kaal: 467 g, 57 Line drawings, color; 57 Illustrations, color
  • Sari: Chapman & Hall/CRC Texts in Statistical Science
  • Ilmumisaeg: 17-Feb-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1032153733
  • ISBN-13: 9781032153735
Teised raamatud teemal:
  • Formaat: Hardback, 190 pages, kõrgus x laius: 234x156 mm, kaal: 467 g, 57 Line drawings, color; 57 Illustrations, color
  • Sari: Chapman & Hall/CRC Texts in Statistical Science
  • Ilmumisaeg: 17-Feb-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1032153733
  • ISBN-13: 9781032153735
Teised raamatud teemal:
"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 vii
Author ix
1 Stochastic Process, Discrete-time Markov Chain
1(42)
1.1 Definition of Stochastic Process
1(1)
1.2 Discrete-time Markov Chain
1(2)
1.3 Chapman-Kolmogorov Equations
3(2)
1.4 Classification of States
5(2)
1.5 Limiting Probabilities
7(2)
1.6 Computations in R
9(5)
1.7 Simulations in R
14(14)
1.8 Applications of Markov Chain
28(9)
Exercises
37(6)
2 Random Walk
43(18)
2.1 Definition of Random Walk
43(2)
2.2 Must-Know. Facts About Random Walk
45(2)
2.3 Simulations in R
47(4)
2.4 Applications of Random Walk
51(6)
Exercises
57(4)
3 Poisson Process
61(20)
3.1 Definition and Must-Know Facts About Poisson Process
61(5)
3.2 Simulations in R
66(4)
3.3 Applications of Poisson Process
70(6)
Exercises
76(5)
4 Nonhomogeneous Poisson Process
81(24)
4.1 Definition of Nonhomogeneous Poisson Process
81(3)
4.2 Simulations in R
84(7)
4.3 Applications of Nonhomogeneous Poisson Process
91(11)
Exercises
102(3)
5 Compound Poisson Process
105(12)
5.1 Definition of Compound Poisson Process
105(2)
5.2 Simulations in R
107(4)
5.3 Applications of Compound Poisson Process
111(2)
Exercises
113(4)
6 Conditional Poisson Process
117(12)
6.1 Definition of Conditional Poisson Process
117(2)
6.2 Simulations in R
119(4)
6.3 Applications of Conditional Poisson Process
123(2)
Exercises
125(4)
7 Birth-and-Death Process
129(12)
7.1 Definition of Birth-and-Death Process
129(3)
7.2 Simulations in R
132(3)
7.3 Applications of Birth-and-Death Process
135(2)
Exercises
137(4)
8 Branching Process
141(12)
8.1 Definition of Branching Process
141(4)
8.2 Simulations in R
145(3)
8.3 Applications of Branching Process
148(1)
Exercises
149(4)
9 Brownian Motion
153(30)
9.1 Definition of Brownian Motion
153(3)
9.2 Processes Derived from Brownian Motion
156(3)
9.2.1 Brownian Bridge
156(1)
9.2.2 Brownian Motion with Drift and Volatility
157(1)
9.2.3 Geometric Brownian Motion
157(1)
9.2.4 The Ornstein-Uhlenbeck Process
158(1)
9.3 Simulations in R
159(8)
9.4 Applications of Brownian Motion
167(10)
Exercises
177(6)
Recommended Books 183(2)
List of Notations 185(2)
Index 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.