08370nam a22003614a 450000100090000000300090000900500170001800800410003501000170007601500190009301600180011202000290013002000260015903500240018504000280020908200150023710000230025224500950027525000120037026000500038230000350043250400510046750509480051850510180146650509870248450510020347150510110447350510400548450507880652452006500731265000260796265000200798816528275BD-KhUET20180909153947.0180909s2011    flua     b    001 0 eng    a  2010043676  aGBB0608392bnb7 a0155512322Uk  a9781439818824 (hardback)  a1439818827 (hardback)  a(OCoLC)ocn615883171  aDLCcDLCdYDXbBD-KhUET00a519.232221 aAllen, Linda J. S.13aAn introduction to stochastic processes with applications to biology /cLinda J. S. Allen.  a2nd ed.  aBoca Raton, FL :bChapman & Hall/CRC,cc2011.  axxiv, 466 p. :bill. ;c25 cm.  aIncludes bibliographical references and index.00gMachine generated contents note:g1.tReview of Probability Theory and an Introduction to Stochastic Processes --g1.1.tIntroduction --g1.2.tBrief Review of Probability Theory --g1.2.1.tBasic Probability Concepts --g1.2.2.tProbability Distributions --g1.2.3.tExpectation --g1.2.4.tMultivariate Distributions --g1.3.tGenerating Functions --g1.4.tCentral Limit Theorem --g1.5.tIntroduction to Stochastic Processes --g1.6.tAn Introductory Example: A Simple Birth Process --g1.7.tExercises for Chapter 1 --g1.8.tReferences for Chapter 1 --g1.9.tAppendix for Chapter 1 --g1.9.1.tProbability Distributions --g1.9.2.tMATLAB® and FORTRAN Programs --g1.9.3.tInterevent Time --g2.tDiscrete-Time Markov Chains --g2.1.tIntroduction --g2.2.tDefinitions and Notation --g2.3.tClassification of States --g2.4.tFirst Passage Time --g2.5.tBasic Theorems for Markov Chains --g2.6.tStationary Probability Distribution00g2.7.tFinite Markov Chains --g2.7.1.tMean First Passage Time --g2.8.tAn Example: Genetics Inbreeding Problem --g2.9.tMonte Carlo Simulation --g2.10.tUnrestricted Random Walk in Higher Dimensions --g2.10.1.tTwo Dimensions --g2.10.2.tThree Dimensions --g2.11.tExercises for Chapter 2 --g2.12.tReferences for Chapter 2 --g2.13.tAppendix for Chapter 2 --g2.13.1.tProofs of Theorems 2.5 and 2.6 --g2.13.2.tPerron and Frobenius Theorems --g2.13.3.tThe n-Step Transition Matrix --g2.13.4.tGenetics Inbreeding Problem --g3.tBiological Applications of Discrete-Time Markov Chains --g3.1.tIntroduction --g3.2.tProliferating Epithelial Cells --g3.3.tRestricted Random Walk Models --g3.4.tRandom Walk with Absorbing Boundaries --g3.4.1.tProbability of Absorption --g3.4.2.tExpected Time until Absorption --g3.4.3.tProbability Distribution for Absorption --g3.5.tRandom Walk on a Semi-Infinite Domain --g3.6.tGeneral Birth and Death Process --g3.6.1.tExpected Time to Extinction00g3.7.tLogistic Growth Process --g3.8.tQuasistationary Probability Distribution --g3.9.tSIS Epidemic Model --g3.9.1.tDeterministic Model --g3.9.2.tStochastic Model --g3.10.tChain Binomial Epidemic Models --g3.10.1.tGreenwood Model --g3.10.2.tReed-Frost Model --g3.10.3.tDuration and Size --g3.11.tExercises for Chapter 3 --g3.12.tReferences for Chapter 3 --g3.13.tAppendix for Chapter 3 --g3.13.1.tMATLAB® Programs --g3.13.2.tMaple™ Program --g4.tDiscrete-Time Branching Processes --g4.1.tIntroduction --g4.2.tDefinitions and Notation --g4.3.tProbability Generating Function of Xn --g4.4.tProbability of Population Extinction --g4.5.tMean and Variance of Xn --g4.6.tEnvironmental Variation --g4.7.tMultitype Branching Processes --g4.7.1.tAn Example: Age-Structured Model --g4.7.2.tEnvironmental Variation --g4.8.tExercises for Chapter 4 --g4.9.tReferences for Chapter 4 --g5.tContinuous-Time Markov Chains --g5.1.tIntroduction00g5.2.tDefinitions and Notation --g5.3.tThe Poisson Process --g5.4.tGenerator Matrix Q --g5.5.tEmbedded Markov Chain and Classification of States --g5.6.tKolmogorov Differential Equations --g5.7.tStationary Probability Distribution --g5.8.tFinite Markov Chains --g5.9.tGenerating Function Technique --g5.10.tInterevent Time and Stochastic Realizations --g5.11.tReview of Method of Characteristics --g5.12.tExercises for Chapter 5 --g5.13.tReferences for Chapter 5 --g5.14.tAppendix for Chapter 5 --g5.14.1.tCalculation of the Matrix Exponential --g5.14.2.tMATLAB® Programs --g6.tContinuous-Time Birth and Death Chains --g6.1.tIntroduction --g6.2.tGeneral Birth and Death Process --g6.3.tStationary Probability Distribution --g6.4.tSimple Birth and Death Processes --g6.4.1.tSimple Birth --g6.4.2.tSimple Death --g6.4.3.tSimple Birth and Death --g6.4.4.tSimple Birth and Death with Immigration --g6.5.tQueueing Process --g6.6.tPopulation Extinction00g6.7.tFirst Passage Time --g6.7.1.tDefinition and Computation --g6.7.2.tSummary of First Passage Time --g6.8.tLogistic Growth Process --g6.9.tQuasistationary Probability Distribution --g6.10.tAn Explosive Birth Process --g6.11.tNonhomogeneous Birth and Death Process --g6.12.tExercises for Chapter 6 --g6.13.tReferences for Chapter 6 --g6.14.tAppendix for Chapter 6 --g6.14.1.tGenerating Functions for the Simple Birth and Death Process --g6.14.2.tProofs of Theorems 6.2 and 6.3 --g6.14.3.tComparison Theorem --g7.tBiological Applications of Continuous-Time Markov Chains --g7.1.tIntroduction --g7.2.tContinuous-Time Branching Processes --g7.3.tSI and SIS Epidemic Processes --g7.3.1.tStochastic SI Model --g7.3.2.tStochastic SIS Model --g7.4.tMultivariate Processes --g7.5.tEnzyme Kinetics --g7.5.1.tDeterministic Model --g7.5.2.tStochastic Model --g7.6.tSIR Epidemic Process --g7.6.1.tDeterministic Model --g7.6.2.tStochastic Model --g7.6.3.tFinal Size00g7.6.4.tDuration --g7.7.tCompetition Process --g7.7.1.tDeterministic Model --g7.7.2.tStochastic Model --g7.8.tPredator-Prey Process --g7.8.1.tDeterministic Model --g7.8.2.tStochastic Model --g7.9.tExercises for Chapter 7 --g7.10.tReferences for Chapter 7 --g7.11.tAppendix for Chapter 7 --g7.11.1.tMATLAB® Programs --g8.tDiffusion Processes and Stochastic Differential Equations --g8.1.tIntroduction --g8.2.tDefinitions and Notation --g8.3.tRandom Walk and Brownian Motion --g8.4.tDiffusion Process --g8.5.tKolmogorov Differential Equations --g8.6.tWiener Process --g8.7.tIto Stochastic Integral --g8.8.tIto Stochastic Differential Equation --g8.9.tFirst Passage Time --g8.10.tNumerical Methods for SDEs --g8.11.tAn Example: Drug Kinetics --g8.12.tExercises for Chapter 8 --g8.13.tReferences for Chapter 8 --g8.14.tAppendix for Chapter 8 --g8.14.1.tDerivation of Kolmogorov Equations --g8.14.2.tMATLAB® Program --g9.tBiological Applications of Stochastic Differential Equations00g9.1.tIntroduction --g9.2.tMultivariate Processes --g9.3.tDerivation of Ito SDEs --g9.4.tScalar Ito SDEs for Populations --g9.4.1.tSimple Birth and Death with Immigration --g9.4.2.tLogistic Growth --g9.4.3.tQuasistationary Density Function --g9.5.tEnzyme Kinetics --g9.6.tSIR Epidemic Process --g9.7.tCompetition Process --g9.8.tPredator-Prey Process --g9.9.tPopulation Genetics Process --g9.10.tExercises for Chapter 9 --g9.11.tReferences for Chapter 9 --g9.12.tAppendix for Chapter 9 --g9.12.1.tMATLAB® Programs --gAppendix AtHints and Solutions to Selected Exercises --gA.1.tChapter 1 --gA.2.tChapter 2 --gA.3.tChapter 3 --gA.4.tChapter 4 --gA.5.tChapter 5 --gA.6.tChapter 6 --gA.7.tChapter 7 --gA.8.tChapter 8 --gA.9.tChapter 9.  a"The second edition of a bestseller, this textbook delineates stochastic processes, emphasizing applications in biology. It includes MATLAB throughout the book to help with the solutions of various problems. The book is organized according to the three types of stochastic processes: discrete time Markov chains, continuous time Markov chains and continuous time and state Markov processes. It contains a new chapter on the biological applications of stochastic differential equations and new sections on alternative methods for derivation of a stochastic differential equation, data and parameter estimation, Monte Carlo simulation, and more"-- 0aStochastic processes. 0aBiomathematics.