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020 _a9781071641729
_9978-1-0716-4172-9
024 7 _a10.1007/978-1-0716-4172-9
_2doi
050 4 _aQA276-280
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
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072 7 _aPBT
_2thema
100 1 _aLange, Kenneth.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_988634
245 1 0 _aApplied Probability
_h[electronic resource] /
_cby Kenneth Lange.
250 _a3rd ed. 2024.
264 1 _aNew York, NY :
_bSpringer US :
_bImprint: Springer,
_c2024.
300 _aXVII, 602 p. 18 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Texts in Statistics,
_x2197-4136
505 0 _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.
520 _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.
650 0 _aStatistics.
_965982
650 0 _aProbabilities.
_965724
650 0 _aComputer science
_xMathematics.
_964041
650 0 _aMathematical statistics.
_967233
650 0 _aMathematics
_xData processing.
_965715
650 1 4 _aStatistical Theory and Methods.
650 2 4 _aProbability Theory.
_967428
650 2 4 _aProbability and Statistics in Computer Science.
_967234
650 2 4 _aComputational Mathematics and Numerical Analysis.
_966073
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9781071641712
776 0 8 _iPrinted edition:
_z9781071641736
776 0 8 _iPrinted edition:
_z9781071641743
830 0 _aSpringer Texts in Statistics,
_x2197-4136
_972551
856 4 0 _uhttps://doi.org/10.1007/978-1-0716-4172-9
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