Introduction to Stochastic Processes with R

Detalles Bibliográficos
Autor principal: Dobrow, Robert P.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2016.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • TITLE PAGE
  • COPYRIGHT
  • DEDICATION
  • TABLE OF CONTENTS
  • PREFACE
  • ACKNOWLEDGMENTS
  • LIST OF SYMBOLS AND NOTATION
  • NOTATION CONVENTIONS
  • ABBREVIATIONS
  • ABOUT THE COMPANION WEBSITE
  • CHAPTER 1: INTRODUCTION AND REVIEW
  • 1.1 DETERMINISTIC AND STOCHASTIC MODELS
  • 1.2 WHAT IS A STOCHASTIC PROCESS?
  • 1.3 MONTE CARLO SIMULATION
  • 1.4 CONDITIONAL PROBABILITY
  • 1.5 CONDITIONAL EXPECTATION
  • CHAPTER 2: MARKOV CHAINS: FIRST STEPS
  • 2.1 INTRODUCTION
  • 2.2 MARKOV CHAIN CORNUCOPIA
  • 2.3 BASIC COMPUTATIONS
  • 2.4 LONG-TERM BEHAVIOR-THE NUMERICAL EVIDENCE
  • 2.5 SIMULATION
  • 2.6 MATHEMATICAL INDUCTION*
  • CHAPTER 3: MARKOV CHAINS FOR THE LONG TERM
  • 3.1 LIMITING DISTRIBUTION
  • 3.2 STATIONARY DISTRIBUTION
  • 3.3 CAN YOU FIND THE WAY TO STATE a?
  • 3.4 IRREDUCIBLE MARKOV CHAINS
  • 3.5 PERIODICITY
  • 3.6 ERGODIC MARKOV CHAINS
  • 3.7 TIME REVERSIBILITY
  • 3.8 ABSORBING CHAINS
  • 3.9 REGENERATION AND THE STRONG MARKOV PROPERTY*
  • 3.10 PROOFS OF LIMIT THEOREMS*
  • CHAPTER 4: BRANCHING PROCESSES
  • 4.1 INTRODUCTION
  • 4.2 MEAN GENERATION SIZE
  • 4.3 PROBABILITY GENERATING FUNCTIONS
  • 4.4 EXTINCTION IS FOREVER
  • CHAPTER 5: MARKOV CHAIN MONTE CARLO
  • 5.1 INTRODUCTION
  • 5.2 METROPOLIS-HASTINGS ALGORITHM
  • 5.3 GIBBS SAMPLER
  • 5.4 PERFECT SAMPLING*
  • 5.5 RATE OF CONVERGENCE: THE EIGENVALUE CONNECTION*
  • 5.6 CARD SHUFFLING AND TOTAL VARIATION DISTANCE*
  • CHAPTER 6: POISSON PROCESS
  • 6.1 INTRODUCTION
  • 6.2 ARRIVAL, INTERARRIVAL TIMES
  • 6.3 INFINITESIMAL PROBABILITIES
  • 6.4 THINNING, SUPERPOSITION
  • 6.5 UNIFORM DISTRIBUTION
  • 6.6 SPATIAL POISSON PROCESS
  • 6.7 NONHOMOGENEOUS POISSON PROCESS
  • 6.8 PARTING PARADOX
  • CHAPTER 7: CONTINUOUS-TIME MARKOV CHAINS
  • 7.1 INTRODUCTION
  • 7.2 ALARM CLOCKS AND TRANSITION RATES
  • 7.3 INFINITESIMAL GENERATOR
  • 7.4 LONG-TERM BEHAVIOR
  • 7.5 TIME REVERSIBILITY
  • 7.6 QUEUEING THEORY
  • 7.7 POISSON SUBORDINATION
  • CHAPTER 8: BROWNIAN MOTION
  • 8.1 INTRODUCTION
  • 8.2 BROWNIAN MOTION AND RANDOM WALK
  • 8.3 GAUSSIAN PROCESS
  • 8.4 TRANSFORMATIONS AND PROPERTIES
  • 8.5 VARIATIONS AND APPLICATIONS
  • 8.6 MARTINGALES
  • CHAPTER 9: A GENTLE INTRODUCTION TO STOCHASTIC CALCULUS*
  • 9.1 INTRODUCTION
  • 9.2 ITO INTEGRAL
  • 9.3 STOCHASTIC DIFFERENTIAL EQUATIONS
  • APPENDIX A: GETTING STARTED WITH R
  • APPENDIX B: PROBABILITY REVIEW
  • B.1 DISCRETE RANDOM VARIABLES
  • B.2 JOINT DISTRIBUTION
  • B.3 CONTINUOUS RANDOM VARIABLES
  • B.4 COMMON PROBABILITY DISTRIBUTIONS
  • B.5 LIMIT THEOREMS
  • B.6 MOMENT-GENERATING FUNCTIONS
  • APPENDIX C: SUMMARY OF COMMON PROBABILITY DISTRIBUTIONS
  • APPENDIX D: MATRIX ALGEBRA REVIEW
  • D.1 BASIC OPERATIONS
  • D.2 LINEAR SYSTEM
  • D.3 MATRIX MULTIPLICATION
  • D.4 DIAGONAL, IDENTITY MATRIX, POLYNOMIALS
  • D.5 TRANSPOSE
  • D.6 INVERTIBILITY
  • D.7 BLOCK MATRICES
  • D.8 LINEAR INDEPENDENCE AND SPAN
  • D.9 BASIS
  • D.10 VECTOR LENGTH
  • D.11 ORTHOGONALITY
  • D.12 EIGENVALUE, EIGENVECTOR
  • D.13 DIAGONALIZATION
  • ANSWERS TO SELECTED ODD-NUMBERED EXERCISES

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