LEADER 01219nam 2200349Ia 450 001 996391560203316 005 20200824125305.0 035 $a(CKB)1000000000677119 035 $a(EEBO)2264206674 035 $a(OCoLC)ocm8252070e 035 $a(OCoLC)8252070 035 $a(EXLCZ)991000000000677119 100 $a19820318d1676 uy | 101 0 $aeng 135 $aurbn||||a|bb| 200 12$aA sermon preached at St. Margarets in Westminster at the funeral of Mrs. Susanna Gray, daughter of Henry Gray, Esq. of Enfield in Staffordshire, who on the 29 of October, 1654, began her eternal sabbath$b[electronic resource] /$fby Robert Waring 210 $aLondon $c[s.n.]$dPrinted in the year 1676 215 $a95 p 300 $aReproduction of original in the Cambridge University Library. 330 $aeebo-0021 606 $aFuneral sermons 606 $aSermons, English$y17th century 615 0$aFuneral sermons. 615 0$aSermons, English 700 $aWaring$b Robert$f1614-1658.$01003722 801 0$bEEU 801 1$bEEU 801 2$bWaOLN 906 $aBOOK 912 $a996391560203316 996 $aA sermon preached at St. Margarets in Westminster$92342499 997 $aUNISA LEADER 05723nam 2200805 a 450 001 9910817355103321 005 20240401164208.0 010 $a9781118617939 010 $a1118617932 010 $a9781118618059 010 $a111861805X 010 $a9781118629857 010 $a111862985X 035 $a(CKB)2550000001111833 035 $a(EBL)1368912 035 $a(SSID)ssj0001034045 035 $a(PQKBManifestationID)11625333 035 $a(PQKBTitleCode)TC0001034045 035 $a(PQKBWorkID)11007550 035 $a(PQKB)11192892 035 $a(DLC) 2013017918 035 $a(Au-PeEL)EBL1368912 035 $a(CaPaEBR)ebr10748669 035 $a(CaONFJC)MIL511725 035 $a(PPN)179863703 035 $a(FR-PaCSA)88819096 035 $a(MiAaPQ)EBC1368912 035 $a(OCoLC)842307629 035 $a(FRCYB88819096)88819096 035 $a(Perlego)1001723 035 $a(EXLCZ)992550000001111833 100 $a20130430d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aElements of random walk and diffusion processes /$fOliver C. Ibe 205 $a1st ed. 210 $aHoboken, N.J. $cJohn Wiley & Sons, Inc.$d2013 215 $a1 online resource (278 p.) 225 0$aWiley series in operations research and management science 300 $aDescription based upon print version of record. 311 08$a9781118618097 311 08$a1118618092 311 08$a9781299804746 311 08$a1299804748 320 $aIncludes bibliographical references and index. 327 $aElements of Random Walk and Diffusion Processes; Copyright; Contents; Preface; Acknowledgments; 1 Review of Probability Theory; 1.1 Introduction; 1.2 Random Variables; 1.2.1 Distribution Functions; 1.2.2 Discrete Random Variables; 1.2.3 Continuous Random Variables; 1.2.4 Expectations; 1.2.5 Moments of Random Variables and the Variance; 1.3 Transform Methods; 1.3.1 The Characteristic Function; 1.3.2 Moment-Generating Property of the Characteristic Function; 1.3.3 The s-Transform; 1.3.4 Moment-Generating Property of the s-Transform; 1.3.5 The z-Transform 327 $a1.3.6 Moment-Generating Property of the z-Transform1.4 Covariance and Correlation Coefficient; 1.5 Sums of Independent Random Variables; 1.6 Some Probability Distributions; 1.6.1 The Bernoulli Distribution; 1.6.2 The Binomial Distribution; 1.6.3 The Geometric Distribution; 1.6.4 The Poisson Distribution; 1.6.5 The Exponential Distribution; 1.6.6 Normal Distribution; 1.7 Limit Theorems; 1.7.1 Markov Inequality; 1.7.2 Chebyshev Inequality; 1.7.3 Laws of Large Numbers; 1.7.4 The Central Limit Theorem; Problems; 2 Overview of Stochastic Processes; 2.1 Introduction 327 $a2.2 Classification of Stochastic Processes2.3 Mean and Autocorrelation Function; 2.4 Stationary Processes; 2.4.1 Strict-Sense Stationary Processes; 2.4.2 Wide-Sense Stationary Processes; 2.5 Power Spectral Density; 2.6 Counting Processes; 2.7 Independent Increment Processes; 2.8 Stationary Increment Process; 2.9 Poisson Processes; 2.9.1 Compound Poisson Process; 2.10 Markov Processes; 2.10.1 Discrete-Time Markov Chains; 2.10.2 State Transition Probability Matrix; 2.10.3 The k-Step State Transition Probability; 2.10.4 State Transition Diagrams; 2.10.5 Classification of States 327 $a2.10.6 Limiting-State Probabilities2.10.7 Doubly Stochastic Matrix; 2.10.8 Continuous-Time Markov Chains; 2.10.9 Birth and Death Processes; 2.11 Gaussian Processes; 2.12 Martingales; 2.12.1 Stopping Times; Problems; 3 One-Dimensional Random Walk; 3.1 Introduction; 3.2 Occupancy Probability; 3.3 Random Walk as a Markov Chain; 3.4 Symmetric Random Walk as a Martingale; 3.5 Random Walk with Barriers; 3.6 Mean-Square Displacement; 3.7 Gambler's Ruin; 3.7.1 Ruin Probability; 3.7.2 Alternative Derivation of Ruin Probability; 3.7.3 Duration of a Game; 3.8 Random Walk with Stay 327 $a3.9 First Return to the Origin3.10 First Passage Times for Symmetric Random Walk; 3.10.1 First Passage Time via the Generating Function; 3.10.2 First Passage Time via the Reflection Principle; 3.10.3 Hitting Time and the Reflection Principle; 3.11 The Ballot Problem and the Reflection Principle; 3.11.1 The Conditional Probability Method; 3.12 Returns to the Origin and the Arc-Sine Law; 3.13 Maximum of a Random Walk; 3.14 Two Symmetric Random Walkers; 3.15 Random Walk on a Graph; 3.15.1 Proximity Measures; 3.15.2 Directed Graphs; 3.15.3 Random Walk on an Undirected Graph 327 $a3.15.4 Random Walk on a Weighted Graph 330 $a"Featuring an introduction to stochastic calculus, this book uniquely blends diffusion equations and random walk theory and provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. It covers standard methods and applications of Brownian motion and discusses Levy motion; addresses fractional calculus; introduces percolation theory and its relationship to diffusion processes; and more"--$cProvided by publisher. 410 0$aWiley Series in Operations Research and Management Science 606 $aRandom walks (Mathematics) 606 $aDiffusion processes 615 0$aRandom walks (Mathematics) 615 0$aDiffusion processes. 676 $a519.2/82 686 $aMAT003000$2bisacsh 700 $aIbe$b Oliver C$g(Oliver Chukwudi),$f1947-$0522175 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817355103321 996 $aElements of random walk and diffusion processes$94034004 997 $aUNINA