{"product_id":"introduction-to-stochastic-processes-with-r-isbn-9781118740651","title":"Introduction to Stochastic Processes with R","description":"\u003cp\u003e\u003cb\u003eAn introduction to stochastic processes through the use of R\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntroduction to Stochastic Processes with R \u003c\/i\u003eis 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.\u003c\/p\u003e \u003cp\u003eWritten 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, \u003ci\u003eIntroduction to Stochastic Processes with R \u003c\/i\u003efeatures:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eMore than 200 examples and 600 end-of-chapter exercises\u003c\/li\u003e \u003cli\u003eA tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra\u003c\/li\u003e \u003cli\u003eDiscussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus\u003c\/li\u003e \u003cli\u003eIntroductions to mathematics as needed in order to suit readers at many mathematical levels\u003c\/li\u003e \u003cli\u003eA companion web site that includes relevant data files as well as all R code and scripts used throughout the book\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eIntroduction to Stochastic Processes with R \u003c\/i\u003eis 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.\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xv\u003c\/p\u003e \u003cp\u003eList of Symbols and Notation xvii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction and Review 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Deterministic and Stochastic Models 1\u003c\/p\u003e \u003cp\u003e1.2 What is a Stochastic Process? 5\u003c\/p\u003e \u003cp\u003e1.3 Monte Carlo Simulation 9\u003c\/p\u003e \u003cp\u003e1.4 Conditional Probability 10\u003c\/p\u003e \u003cp\u003e1.5 Conditional Expectation 18\u003c\/p\u003e \u003cp\u003eExercises 34\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Markov Chains: First Steps 40\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 40\u003c\/p\u003e \u003cp\u003e2.2 Markov Chain Cornucopia 42\u003c\/p\u003e \u003cp\u003e2.3 Basic Computations 52\u003c\/p\u003e \u003cp\u003e2.4 Long-Term Behavior—the Numerical Evidence 59\u003c\/p\u003e \u003cp\u003e2.5 Simulation 65\u003c\/p\u003e \u003cp\u003e2.6 Mathematical Induction* 68\u003c\/p\u003e \u003cp\u003eExercises 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Markov Chains for the Long Term 76\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Limiting Distribution 76\u003c\/p\u003e \u003cp\u003e3.2 Stationary Distribution 80\u003c\/p\u003e \u003cp\u003e3.3 Can you Find the Way to State a? 94\u003c\/p\u003e \u003cp\u003e3.4 Irreducible Markov Chains 103\u003c\/p\u003e \u003cp\u003e3.5 Periodicity 106\u003c\/p\u003e \u003cp\u003e3.6 Ergodic Markov Chains 109\u003c\/p\u003e \u003cp\u003e3.7 Time Reversibility 114\u003c\/p\u003e \u003cp\u003e3.8 Absorbing Chains 119\u003c\/p\u003e \u003cp\u003e3.9 Regeneration and the Strong Markov Property* 133\u003c\/p\u003e \u003cp\u003e3.10 Proofs of Limit Theorems* 135\u003c\/p\u003e \u003cp\u003eExercises 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Branching Processes 158\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 158\u003c\/p\u003e \u003cp\u003e4.2 Mean Generation Size 160\u003c\/p\u003e \u003cp\u003e4.3 Probability Generating Functions 164\u003c\/p\u003e \u003cp\u003e4.4 Extinction is Forever 168\u003c\/p\u003e \u003cp\u003eExercises 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Markov Chain Monte Carlo 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 181\u003c\/p\u003e \u003cp\u003e5.2 Metropolis–Hastings Algorithm 187\u003c\/p\u003e \u003cp\u003e5.3 Gibbs Sampler 197\u003c\/p\u003e \u003cp\u003e5.4 Perfect Sampling* 205\u003c\/p\u003e \u003cp\u003e5.5 Rate of Convergence: the Eigenvalue Connection* 210\u003c\/p\u003e \u003cp\u003e5.6 Card Shuffling and Total Variation Distance* 212\u003c\/p\u003e \u003cp\u003eExercises 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Poisson Process 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 223\u003c\/p\u003e \u003cp\u003e6.2 Arrival, Interarrival Times 227\u003c\/p\u003e \u003cp\u003e6.3 Infinitesimal Probabilities 234\u003c\/p\u003e \u003cp\u003e6.4 Thinning, Superposition 238\u003c\/p\u003e \u003cp\u003e6.5 Uniform Distribution 243\u003c\/p\u003e \u003cp\u003e6.6 Spatial Poisson Process 249\u003c\/p\u003e \u003cp\u003e6.7 Nonhomogeneous Poisson Process 253\u003c\/p\u003e \u003cp\u003e6.8 Parting Paradox 255\u003c\/p\u003e \u003cp\u003eExercises 258\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Continuous-Time Markov Chains 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 265\u003c\/p\u003e \u003cp\u003e7.2 Alarm Clocks and Transition Rates 270\u003c\/p\u003e \u003cp\u003e7.3 Infinitesimal Generator 273\u003c\/p\u003e \u003cp\u003e7.4 Long-Term Behavior 283\u003c\/p\u003e \u003cp\u003e7.5 Time Reversibility 294\u003c\/p\u003e \u003cp\u003e7.6 Queueing Theory 301\u003c\/p\u003e \u003cp\u003e7.7 Poisson Subordination 306\u003c\/p\u003e \u003cp\u003eExercises 313\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Brownian Motion 320\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 320\u003c\/p\u003e \u003cp\u003e8.2 Brownian Motion and Random Walk 326\u003c\/p\u003e \u003cp\u003e8.3 Gaussian Process 330\u003c\/p\u003e \u003cp\u003e8.4 Transformations and Properties 334\u003c\/p\u003e \u003cp\u003e8.5 Variations and Applications 345\u003c\/p\u003e \u003cp\u003e8.6 Martingales 356\u003c\/p\u003e \u003cp\u003eExercises 366\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 A Gentle Introduction to Stochastic Calculus* 372\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 372\u003c\/p\u003e \u003cp\u003e9.2 Ito Integral 378\u003c\/p\u003e \u003cp\u003e9.3 Stochastic Differential Equations 385\u003c\/p\u003e \u003cp\u003eExercises 397\u003c\/p\u003e \u003cp\u003eA Getting Started with R 400\u003c\/p\u003e \u003cp\u003eB Probability Review 421\u003c\/p\u003e \u003cp\u003eB.1 Discrete Random Variables 422\u003c\/p\u003e \u003cp\u003eB.2 Joint Distribution 424\u003c\/p\u003e \u003cp\u003eB.3 Continuous Random Variables 426\u003c\/p\u003e \u003cp\u003eB.4 Common Probability Distributions 428\u003c\/p\u003e \u003cp\u003eB.5 Limit Theorems 439\u003c\/p\u003e \u003cp\u003eB.6 Moment-Generating Functions 440\u003c\/p\u003e \u003cp\u003eC Summary of Common Probability Distributions 443\u003c\/p\u003e \u003cp\u003eD Matrix Algebra Review 445\u003c\/p\u003e \u003cp\u003eD.1 Basic Operations 445\u003c\/p\u003e \u003cp\u003eD.2 Linear System 447\u003c\/p\u003e \u003cp\u003eD.3 Matrix Multiplication 448\u003c\/p\u003e \u003cp\u003eD.4 Diagonal, Identity Matrix, Polynomials 448\u003c\/p\u003e \u003cp\u003eD.5 Transpose 449\u003c\/p\u003e \u003cp\u003eD.6 Invertibility 449\u003c\/p\u003e \u003cp\u003eD.7 Block Matrices 449\u003c\/p\u003e \u003cp\u003eD.8 Linear Independence and Span 450\u003c\/p\u003e \u003cp\u003eD.9 Basis 451\u003c\/p\u003e \u003cp\u003eD.10 Vector Length 451\u003c\/p\u003e \u003cp\u003eD.11 Orthogonality 452\u003c\/p\u003e \u003cp\u003eD.12 Eigenvalue, Eigenvector 452\u003c\/p\u003e \u003cp\u003eD.13 Diagonalization 453\u003c\/p\u003e \u003cp\u003eAnswers to Selected Odd-Numbered Exercises 455\u003c\/p\u003e \u003cp\u003eReferences 470\u003c\/p\u003e \u003cp\u003eIndex 475\u003c\/p\u003e \"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\" \u003cb\u003eThomas Polaski, Mathematical Reviews, Sept 2017\u003c\/b\u003e \u003cb\u003eRobert P. Dobrow, PhD,\u003c\/b\u003e 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. \u003cp\u003e\u003cb\u003eAn introduction to stochastic processes through the use of R\u003cbr\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntroduction to Stochastic Processes with R\u003c\/i\u003e 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 freeware R, makes theoretical results come alive with practical, hands-on demonstrations.\u003c\/p\u003e \u003cp\u003eWritten 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, \u003ci\u003eIntroduction to Stochastic Processes with R \u003c\/i\u003efeatures:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eOver 200 examples and 600 end-of-chapter exercises\u003c\/li\u003e \u003cli\u003eA tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra\u003c\/li\u003e \u003cli\u003eDiscussions of many timely and interesting supplemental topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black-Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus\u003c\/li\u003e \u003cli\u003eIntroductions to mathematics as needed in order to suit readers at many mathematical levels\u003c\/li\u003e \u003cli\u003eA companion website that includes relevant data files as well as all R code and scripts used throughout the book\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eIntroduction to Stochastic Processes with R \u003c\/i\u003eis 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989467414757,"sku":"NP9781118740651","price":106.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118740651.jpg?v=1761784216","url":"https:\/\/k12savings.com\/products\/introduction-to-stochastic-processes-with-r-isbn-9781118740651","provider":"K12savings","version":"1.0","type":"link"}