LEADER 01265nam a2200337 i 4500 001 991001202729707536 005 20020507185136.0 008 001108s1991 uk ||| | eng 020 $a0521400961 035 $ab10814991-39ule_inst 035 $aLE01308633$9ExL 040 $aDip.to Matematica$beng 082 0 $a515.724 084 $aAMS 47L 084 $aQA326.S26 100 1 $aSakai, Shoichiro$050347 245 10$aOperator algebras in dynamical systems :$bthe theory of unbounded derivations in C*-algebras /$cShoichiro Sakai 260 $aCambridge [England] ; New York :$bCambridge University Press,$c1991 300 $axi, 219 p. :$bill. ;$c24 cm. 490 0 $aEncyclopaedia of mathematics and its applications ;$v41 500 $aIncludes bibliographical references 650 0$aC*-algebras 650 0$aDifferentiable dynamical systems 650 0$aHarmonic analysis 650 0$aOperator theory 907 $a.b10814991$b23-02-17$c28-06-02 912 $a991001202729707536 945 $aLE013 47L SAK11 (1991)$g1$i2013000123844$lle013$o-$pE0.00$q-$rl$s- $t0$u1$v0$w1$x0$y.i10920997$z28-06-02 996 $aOperator algebras in dynamical systems$9337822 997 $aUNISALENTO 998 $ale013$b01-01-00$cm$da $e-$feng$guk $h0$i1 LEADER 07178nam 22006255 450 001 9910568249603321 005 20250417030534.0 010 $a3-030-97963-6 024 7 $a10.1007/978-3-030-97963-8 035 $a(MiAaPQ)EBC6975909 035 $a(Au-PeEL)EBL6975909 035 $a(CKB)21957562900041 035 $a(OCoLC)1314629464 035 $a(PPN)269154973 035 $a(DE-He213)978-3-030-97963-8 035 $a(EXLCZ)9921957562900041 100 $a20220504d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aApplied Probability $eFrom Random Experiments to Random Sequences and Statistics /$fby Valérie Girardin, Nikolaos Limnios 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (265 pages) 311 08$aPrint version: Girardin, Valérie Applied Probability Cham : Springer International Publishing AG,c2022 9783030979621 327 $aIntro -- Preface -- Contents -- Notation -- 1 Events and Probability Spaces -- 1.1 Sample Space -- 1.2 Measure Spaces -- 1.2.1 ?-Algebras -- Properties of ?-Algebras -- 1.2.2 Measures -- Properties of Measures -- Dirac Measure -- Counting Measure -- Lebesgue Measure -- 1.3 Probability Spaces -- 1.3.1 General Case -- 1.3.2 Conditional Probabilities -- 1.3.3 Discrete Case: Combinatorial Analysis and Entropy -- Properties of Shannon Entropy -- 1.4 Independence of Finite Collections -- 1.5 Exercises -- 2 Random Variables -- 2.1 Random Variables -- 2.1.1 Measurable Functions -- Properties of Measurable Functions -- 2.1.2 Distributions and Distribution Functions -- Properties of Distribution Functions -- Properties of Quantiles -- 2.2 Expectation -- 2.2.1 Lebesgue Integral -- Properties of Lebesgue Integrals -- 2.2.2 Expectation -- 2.3 Discrete Random Variables -- 2.3.1 General Properties -- 2.3.2 Classical Discrete Distributions -- Dirac Distribution -- Uniform Distribution -- Bernoulli Distribution -- Binomial Distribution -- Hyper-Geometric Distribution -- Geometric and Negative Binomial Distributions -- Poisson Distribution -- 2.4 Continuous Random Variables -- 2.4.1 Absolute Continuity of Measures -- 2.4.2 Densities -- Properties of Densities of Random Variables -- 2.4.3 Classical Distributions with Densities -- Uniform Distribution -- Gaussian Distribution -- Gamma, Exponential, Chi-Squared, Erlang Distributions -- Log-Normal Distribution -- Weibull Distribution -- Inverse-Gaussian Distribution -- Beta Distribution -- Fisher Distribution -- Student and Cauchy Distributions -- 2.4.4 Determination of Distributions -- 2.5 Analytical Tools -- 2.5.1 Generating Functions -- Properties of Generating Functions -- 2.5.2 Fourier Transform and Characteristic Functions -- Properties of Characteristic Functions -- 2.5.3 Laplace Transform. 327 $aProperties of Laplace Transforms -- 2.5.4 Moment Generating Functions and Cramér Transform -- Properties of Cramér Transform -- 2.6 Reliability and Survival Analysis -- 2.7 Exercises and Complements -- 3 Random Vectors -- 3.1 Relations Between Random Variables -- 3.1.1 Covariance -- Properties of Covariance and Correlation Coefficients -- 3.1.2 Independence of Random Variables -- 3.1.3 Stochastic Order Relation -- 3.1.4 Entropy -- Properties of Entropy -- 3.2 Characteristics of Random Vectors -- 3.2.1 Product of Probability Spaces -- 3.2.2 Distribution of Random Vectors -- Properties of Multi-dimensional Distribution Functions -- Properties of Densities of Random Vectors -- Properties of Covariance Matrices -- 3.2.3 Independence of Random Vectors -- Properties of Covariance Matrices of Two Vectors -- 3.3 Functions of Random Vectors -- 3.3.1 Order Statistics -- 3.3.2 Sums of Independent Variables or Vectors -- Properties of Convolution -- 3.3.3 Determination of Distributions -- 3.4 Gaussian Vectors -- 3.5 Exercises and Complements -- 4 Random Sequences -- 4.1 Enumerable Sequences -- 4.1.1 Sequences of Events -- Properties of Superior and Inferior Limits of Events -- 4.1.2 Independence of Sequences -- 4.2 Stochastic Convergence -- 4.2.1 Different Types of Convergence -- 4.2.2 Convergence Criteria -- 4.2.3 Links Between Convergences -- 4.2.4 Convergence of Sequences of Random Vectors -- 4.3 Limit Theorems -- 4.3.1 Asymptotics of Discrete Distributions -- 4.3.2 Laws of Large Numbers -- 4.3.3 Central Limit Theorem -- 4.4 Stochastic Simulation Methods -- 4.4.1 Generating Random Variables -- 4.4.2 Monte Carlo Simulation Method -- 4.5 Exercises and Complements -- 5 Introduction to Statistics -- 5.1 Non-parametric Statistics -- 5.1.1 Empirical Distribution Function -- 5.1.2 Confidence Intervals -- 5.1.3 Non-parametric Testing -- 5.2 Parametric Statistics. 327 $a5.2.1 Point Estimation -- 5.2.2 Maximum Likelihood Method -- 5.2.3 Precision of the Estimators -- 5.2.4 Parametric Confidence Intervals -- 5.2.5 Testing in a Parametric Model -- 5.3 The Linear Model -- 5.3.1 Linear and Quadratic Approximations -- 5.3.2 The Simple Linear Model -- 5.3.3 ANOVA -- For Two Samples -- One Way Model -- Two Way Model -- 5.4 Exercises and Complements -- Further Reading -- Measure and Probability -- Probability Theory and Statistics -- Applications -- Index. 330 $aThis textbook presents the basics of probability and statistical estimation, with a view to applications. The didactic presentation follows a path of increasing complexity with a constant concern for pedagogy, from the most classical formulas of probability theory to the asymptotics of independent random sequences and an introduction to inferential statistics. The necessary basics on measure theory are included to ensure the book is self-contained. Illustrations are provided from many applied fields, including information theory and reliability theory. Numerous examples and exercises in each chapter, all with solutions, add to the main content of the book. Written in an accessible yet rigorous style, the book is addressed to advanced undergraduate students in mathematics and graduate students in applied mathematics and statistics. It will also appeal to students and researchers in other disciplines, including computer science, engineering, biology, physicsand economics, who are interested in a pragmatic introduction to the probability modeling of random phenomena. 606 $aProbabilities 606 $aStatistics 606 $aStatistics 606 $aProbability Theory 606 $aStatistical Theory and Methods 606 $aApplied Probability 606 $aApplied Statistics 615 0$aProbabilities. 615 0$aStatistics. 615 0$aStatistics. 615 14$aProbability Theory. 615 24$aStatistical Theory and Methods. 615 24$aApplied Probability. 615 24$aApplied Statistics. 676 $a519.2 700 $aGirardin$b Vale?rie$0768207 702 $aLimnios$b N. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910568249603321 996 $aApplied Probability$92070204 997 $aUNINA