04038nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183072001500206100007700221245006800298250001800366264006100384300006500445336002600510337002600536338003600562347002400598490004500622505043900667520188001106650001602986650001903002650003503021650002903056650003403085650003603119650002403155650005203179650005403231710003403285773002603319776003603345776003603381776003603417830004503453856004603498978-1-0716-4172-9DE-He21320251030114606.0cr nn 008mamaa241207s2024    xxu|    s    |||| 0|eng d  a97810716417297 a10.1007/978-1-0716-4172-92doi 4aQA276-280 7aPBT2bicssc 7aMAT0290002bisacsh 7aPBT2thema1 aLange, Kenneth.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aApplied Probabilityh[electronic resource] /cby Kenneth Lange.  a3rd ed. 2024. 1aNew York, NY :bSpringer US :bImprint: Springer,c2024.  aXVII, 602 p. 18 illus., 1 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Texts in Statistics,x2197-41360 aBasic Notions of Probability Theory -- Calculation of Expectations -- Convexity, Optimization, and Inequalities -- Combinatorics -- Combinatorial Optimization -- Poisson Processes -- Discrete-Time Markov Chains -- Continuous-Time Markov Chains -- Branching Processes -- Martingales -- Diffusion Processes -- Asymptotic Methods -- Numerical Methods -- Poisson Approximation -- Number Theory -- Entropy -- Appendix: Mathematical Review.  aApplied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. This third edition includes new topics and many worked exercises. The new chapter on entropy stresses Shannon entropy and its mathematical applications. New sections in existing chapters explain the Chinese restaurant problem, the infinite alleles model, saddlepoint approximations, and recurrence relations. The extensive list of new problems pursues topics such as random graph theory omitted in the previous editions. Computational probability receives even greater emphasis than earlier. Some of the solved problems are coding exercises, and Julia code is provided. Mathematical scientists from a variety of backgrounds will find Applied Probability appealing as a reference. This updated edition can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. 0aStatistics. 0aProbabilities. 0aComputer sciencexMathematics. 0aMathematical statistics. 0aMathematicsxData processing.14aStatistical Theory and Methods.24aProbability Theory.24aProbability and Statistics in Computer Science.24aComputational Mathematics and Numerical Analysis.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978107164171208iPrinted edition:z978107164173608iPrinted edition:z9781071641743 0aSpringer Texts in Statistics,x2197-413640uhttps://doi.org/10.1007/978-1-0716-4172-9