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001 BDZ0009873610
003 StDuBDS
005 20190531161549.0
008 101102s2011 flua b 001 0 eng d
010 _a2010043676
020 _a9781439818824:
_c£39.99
020 _a1439818827
035 _a(OCoLC)ocn615883171
040 _aStDuBDS
_beng
_cStDuBDS
_dUk
_dStDuBDSZ
050 0 _b.A63 2011
072 7 _aPS
_2thema
072 7 _aPBWL
_2thema
072 7 _aPBW
_2thema
072 7 _aPBT
_2thema
082 _a519.23
100 1 _aAllen, Linda J. S.
245 1 3 _aAn introduction to stochastic processes with applications to biology /
_cLinda J. S. Allen.
250 _a2nd ed.
260 _aBoca Raton, Fla. :
_bCRC,
_cc2011.
300 _axxiv, 466 p. :
_bill. ;
_c25 cm.
500 _aFormerly CIP.
_5Uk
504 _aIncludes bibliographical references and index.
505 0 0 _gMachine 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 Distribution
505 0 0 _g2.7.
_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 Extinction
505 0 0 _g3.7.
_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.
_tIntroduction
505 0 0 _g5.2.
_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 Extinction
505 0 0 _g6.7.
_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 Size
505 0 0 _g7.6.4.
_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 Equations
505 0 0 _g9.1.
_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 A
_tHints 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.
520 _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"
650 0 _aStochastic processes.
_97810
650 0 _aBiomathematics.
_91723
650 7 _aBiology, life sciences
_2thema
650 7 _aStochastics
_2thema
650 7 _aApplied mathematics
_2thema
650 7 _aProbability & statistics
_2thema
902 _a160808
907 _a.b10410946
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