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E-raamat: Introduction to Stochastic Processes with R

  • Formaat: PDF+DRM
  • Ilmumisaeg: 06-Apr-2016
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118740729
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 06-Apr-2016
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118740729
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An introduction to stochastic processes through the use of R

Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations.

Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features:





More than 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, BlackScholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion web site that includes relevant data files as well as all R code and scripts used throughout the book

Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.

Arvustused

"This text provides an excellent introduction to stochastic processes and their applications"...."Examples are plentiful and well chosen, and help to organize the material and to move it forward. Each section contains a good supply of exercises, both calculational and theoretical" Thomas Polaski, Mathematical Reviews, Sept 2017

Preface xi
Acknowledgments xv
List of Symbols and Notation
xvii
About the Companion Website xxi
1 Introduction and Review
1(39)
1.1 Deterministic and Stochastic Models
1(5)
1.2 What is a Stochastic Process?
6(3)
1.3 Monte Carlo Simulation
9(1)
1.4 Conditional Probability
10(8)
1.5 Conditional Expectation
18(22)
Exercises
34(6)
2 Markov Chains: First Steps
40(36)
2.1 Introduction
40(2)
2.2 Markov Chain Cornucopia
42(10)
2.3 Basic Computations
52(7)
2.4 Long-Term Behavior---the Numerical Evidence
59(6)
2.5 Simulation
65(3)
2.6 Mathematical Induction*
68(8)
Exercises
70(6)
3 Markov Chains for the Long Term
76(82)
3.1 Limiting Distribution
76(4)
3.2 Stationary Distribution
80(14)
3.3 Can you Find the Way to State a?
94(9)
3.4 Irreducible Markov Chains
103(3)
3.5 Periodicity
106(3)
3.6 Ergodic Markov Chains
109(5)
3.7 Time Reversibility
114(5)
3.8 Absorbing Chains
119(14)
3.9 Regeneration and the Strong Markov Property*
133(2)
3.10 Proofs of Limit Theorems*
135(23)
Exercises
144(14)
4 Branching Processes
158(23)
4.1 Introduction
158(2)
4.2 Mean Generation Size
160(4)
4.3 Probability Generating Functions
164(4)
4.4 Extinction is Forever
168(13)
Exercises
175(6)
5 Markov Chain Monte Carlo
181(42)
5.1 Introduction
181(6)
5.2 Metropolis--Hastings Algorithm
187(10)
5.3 Gibbs Sampler
197(8)
5.4 Perfect Sampling*
205(5)
5.5 Rate of Convergence: the Eigenvalue Connection*
210(2)
5.6 Card Shuffling and Total Variation Distance*
212(11)
Exercises
219(4)
6 Poisson Process
223(42)
6.1 Introduction
223(4)
6.2 Arrival, Interarrival Times
227(7)
6.3 Infinitesimal Probabilities
234(4)
6.4 Thinning, Superposition
238(5)
6.5 Uniform Distribution
243(6)
6.6 Spatial Poisson Process
249(4)
6.7 Nonhomogeneous Poisson Process
253(2)
6.8 Parting Paradox
255(10)
Exercises
258(7)
7 Continuous-Time Markov Chains
265(55)
7.1 Introduction
265(5)
7.2 Alarm Clocks and Transition Rates
270(3)
7.3 Infinitesimal Generator
273(10)
7.4 Long-Term Behavior
283(11)
7.5 Time Reversibility
294(7)
7.6 Queueing Theory
301(5)
7.7 Poisson Subordination
306(14)
Exercises
313(7)
8 Brownian Motion
320(52)
8.1 Introduction
320(6)
8.2 Brownian Motion and Random Walk
326(4)
8.3 Gaussian Process
330(4)
8.4 Transformations and Properties
334(11)
8.5 Variations and Applications
345(11)
8.6 Martingales
356(16)
Exercises
366(6)
9 A Gentle Introduction to Stochastic Calculus*
372(28)
9.1 Introduction
372(6)
9.2 Ito Integral
378(7)
9.3 Stochastic Differential Equations
385(15)
Exercises
397(3)
A Getting Started with R
400(21)
B Probability Review
421(22)
B.1 Discrete Random Variables
422(2)
B.2 Joint Distribution
424(2)
B.3 Continuous Random Variables
426(2)
B.4 Common Probability Distributions
428(11)
B.5 Limit Theorems
439(1)
B.6 Moment-Generating Functions
440(3)
C Summary of Common Probability Distributions
443(2)
D Matrix Algebra Review
445(10)
D.1 Basic Operations
445(2)
D.2 Linear System
447(1)
D.3 Matrix Multiplication
448(1)
D.4 Diagonal, Identity Matrix, Polynomials
448(1)
D.5 Transpose
449(1)
D.6 Invertibility
449(1)
D.7 Block Matrices
449(1)
D.8 Linear Independence and Span
450(1)
D.9 Basis
451(1)
D.10 Vector Length
451(1)
D.11 Orthogonality
452(1)
D.12 Eigenvalue, Eigenvector
452(1)
D.13 Diagonalization
453(2)
Answers to Selected Odd-Numbered Exercises 455(15)
References 470(5)
Index 475
Robert P. Dobrow, PhD, is Professor of Mathematics and Statistics at Carleton College. He has taught probability and stochastic processes for over 15 years and has authored numerous research papers in Markov chains, probability theory and statistics.