Introduction to stochastic processes with R. (2016)
- Record Type:
- Book
- Title:
- Introduction to stochastic processes with R. (2016)
- Main Title:
- Introduction to stochastic processes with R
- Further Information:
- Note: Robert P. Dobrow.
- Authors:
- Dobrow, Robert P
- Contents:
- Preface xi Acknowledgments xv List of Symbols and Notation xvii 1 Introduction and Review 1 1.1 Deterministic and Stochastic Models 1 1.2 What is a Stochastic Process? 6 1.3 Monte Carlo Simulation 10 1.4 Conditional Probability 11 1.5 Conditional Expectation 19 Exercises 36 2 Markov Chains: First Steps 41 2.1 Introduction 41 2.2 Markov Chain Cornucopia 43 2.3 Basic Computations 53 2.4 LongTerm Behavior— the Numerical Evidence 61 2.5 Simulation 67 2.6 Mathematical Induction* 71 Exercises 73 3 Markov Chains for the Long Term 79 3.1 Limiting Distribution 79 3.2 Stationary Distribution 83 3.3 Can You Find the Way to State a? 98 3.4 Irreducible Markov Chains 108 3.5 Periodicity 111 3.6 Ergodic Markov Chains 114 3.7 Time Reversibility 119 3.8 Absorbing Chains 124 3.9 Regeneration and the Strong Markov Property* 140 3.10 Proofs of Limit Theorems* 141 Exercises 152 4 Branching Processes 167 4.1 Introduction 167 4.2 Mean Generation Size 169 4.3 Probability Generating Functions 174 4.4 Extinction is Forever 178 Exercises 185 5 Markov Chain Monte Carlo 191 5.1 Introduction 191 5.2 MetropolisHastings Algorithm 197 5.3 Gibbs Sampler 208 5.4 Perfect Sampling* 216 5.5 Rate of Convergence: the Eigenvalue Connection* 222 5.6 Card Shuffling and Total Variation Distance* 224 Exercises 231 6 Poisson Process 235 6.1 Introduction 235 6.2 Arrival, Interarrival Times 239 6.3 Infinitesimal Probabilities 246 6.4 Thinning, Superposition 250 6.5 Uniform Distribution 256 6.6 Spatial Poisson Process 261Preface xi Acknowledgments xv List of Symbols and Notation xvii 1 Introduction and Review 1 1.1 Deterministic and Stochastic Models 1 1.2 What is a Stochastic Process? 6 1.3 Monte Carlo Simulation 10 1.4 Conditional Probability 11 1.5 Conditional Expectation 19 Exercises 36 2 Markov Chains: First Steps 41 2.1 Introduction 41 2.2 Markov Chain Cornucopia 43 2.3 Basic Computations 53 2.4 LongTerm Behavior— the Numerical Evidence 61 2.5 Simulation 67 2.6 Mathematical Induction* 71 Exercises 73 3 Markov Chains for the Long Term 79 3.1 Limiting Distribution 79 3.2 Stationary Distribution 83 3.3 Can You Find the Way to State a? 98 3.4 Irreducible Markov Chains 108 3.5 Periodicity 111 3.6 Ergodic Markov Chains 114 3.7 Time Reversibility 119 3.8 Absorbing Chains 124 3.9 Regeneration and the Strong Markov Property* 140 3.10 Proofs of Limit Theorems* 141 Exercises 152 4 Branching Processes 167 4.1 Introduction 167 4.2 Mean Generation Size 169 4.3 Probability Generating Functions 174 4.4 Extinction is Forever 178 Exercises 185 5 Markov Chain Monte Carlo 191 5.1 Introduction 191 5.2 MetropolisHastings Algorithm 197 5.3 Gibbs Sampler 208 5.4 Perfect Sampling* 216 5.5 Rate of Convergence: the Eigenvalue Connection* 222 5.6 Card Shuffling and Total Variation Distance* 224 Exercises 231 6 Poisson Process 235 6.1 Introduction 235 6.2 Arrival, Interarrival Times 239 6.3 Infinitesimal Probabilities 246 6.4 Thinning, Superposition 250 6.5 Uniform Distribution 256 6.6 Spatial Poisson Process 261 6.7 NonHomogeneous Poisson Process 265 6.8 Parting Paradox 267 Exercises 271 7 ContinuousTime Markov Chains 277 7.1 Introduction 277 7.2 Alarm Clocks and Transition Rates 283 7.3 Infinitesimal Generator 286 7.4 LongTerm Behavior 297 7.5 Time Reversibility 308 7.6 Queueing Theory 316 7.7 Poisson Subordination 322 Exercises 329 8 Brownian Motion 337 8.1 Introduction 337 8.2 Brownian Motion and Random Walk 343 8.3 Gaussian Process 347 8.4 Transformations and Properties 351 8.5 Variations and Applications 363 8.6 Martingales 375 Exercises 386 9 A Gentle Introduction to Stochastic Calculus* 393 9.1 Introduction 393 9.2 Ito Integral 401 9.3 Stochastic Differential Equations 407 Exercises 420 Appendices 422 A Getting Started with R 423 B Probability Review 445 B.1 Discrete Random Variables 446 B.2 Joint Distribution 448 B.3 Continuous Random Variables 451 B.4 Common Probability Distributions 452 B.5 Limit Theorems 463 B.6 MomentGenerating Functions 464 C Summary of Probability Distributions 467 D Matrix Algebra Review 469 Problem Solutions 481 References 497 Index 501 … (more)
- Edition:
- 1st
- Publisher Details:
- Hoboken, New Jersey : John Wiley & Sons, Inc
- Publication Date:
- 2016
- Extent:
- 1 online resource
- Subjects:
- 519.2302855133
Stochastic processes -- Data processing
R (Computer program language) - Languages:
- English
- ISBNs:
- 9781118740705
9781118740729
9781118740583 - Related ISBNs:
- 9781118740651
- Notes:
- Note: Includes bibliographical references and index.
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- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.52144
- Ingest File:
- 02_020.xml