LEADER 04104nam 2200565 450 001 9910485151603321 005 20220321155619.0 010 $a3-030-56402-9 024 7 $a10.1007/978-3-030-56402-5 035 $a(CKB)5590000000005426 035 $a(MiAaPQ)EBC6382110 035 $a(DE-He213)978-3-030-56402-5 035 $a(MiAaPQ)EBC6647529 035 $a(Au-PeEL)EBL6382110 035 $a(OCoLC)1202751794 035 $a(Au-PeEL)EBL6647529 035 $a(PPN)255251467 035 $a(EXLCZ)995590000000005426 100 $a20220321d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProbability theory $ea comprehensive course /$fAchim Klenke 205 $aThird edition. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XIV, 716 p. 55 illus., 24 illus. in color.) 225 1 $aUniversitext,$x0172-5939 311 $a3-030-56401-0 320 $aIncludes bibliographical references and index. 327 $a1 Basic Measure Theory -- 2 Independence -- 3 Generating Functions -- 4 The Integral -- 5 Moments and Laws of Large Numbers -- 6 Convergence Theorems -- 7 Lp-Spaces and the Radon?Nikodym Theorem -- 8 Conditional Expectations -- 9 Martingales -- 10 Optional Sampling Theorems -- 11 Martingale Convergence Theorems and Their Applications -- 12 Backwards Martingales and Exchangeability -- 13 Convergence of Measures -- 14 Probability Measures on Product Spaces -- 15 Characteristic Functions and the Central Limit Theorem -- 16 Infinitely Divisible Distributions -- 17 Markov Chains -- 18 Convergence of Markov Chains -- 19 Markov Chains and Electrical Networks -- 20 Ergodic Theory -- 21 Brownian Motion -- 22 Law of the Iterated Logarithm -- 23 Large Deviations -- 24 The Poisson Point Process -- 25 The Itô Integral -- 26 Stochastic Differential Equations -- References -- Notation Index -- Name Index -- Subject Index. 330 $aThis popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory. Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts. This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aDistribution (Probability theory) 606 $aMeasure theory 615 0$aProbabilities. 615 0$aDistribution (Probability theory) 615 0$aMeasure theory. 676 $a519.2 700 $aKlenke$b Achim$0478404 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910485151603321 996 $aProbability theory$9264282 997 $aUNINA LEADER 04692nam 22005172 450 001 9910776180803321 005 20231204232500.0 010 $a90-04-52306-5 024 7 $a10.1163/9789004523067 035 $a(CKB)5690000000105418 035 $z(OCoLC)1330689464 035 $a(nllekb)BRILL9789004523067 035 $a(MiAaPQ)EBC31218086 035 $a(Au-PeEL)EBL31218086 035 $a(EXLCZ)995690000000105418 100 $a20220630d2022 uy 0 101 0 $aeng 135 $aurun####uuuua 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $2rdacarrier 200 02$aA critical Companion to the 'Mirrors for Princes' Literature /$fedited by Noëlle-Laetitia Perret and Stéphane Péquignot 205 $a1st ed. 210 1$aLeiden ;$aBoston :$cBrill,$d2022. 215 $a1 online resource 225 1 $aReading Medieval Sources ;$v7 311 $a90-04-51875-4 320 $aIncludes bibliographical references and index. 327 $aIdeal models and anti-models of kingship in ancient Greek literature : mirror of princes from Homer to Marcus Aurelius / John R. Lenz -- Greek and Roman writers on the virtues of good rulers : praise, instruction, and constraint / Tom Stevenson -- Carolingian mirrors for princes : texts, contents, impact / Karl Ubl -- Byzantine mirrors for princes : an overview / Gu?nter Prinzing -- The conception of power in Islam : Persian mirrors of princes and Sunni theories (11th-14th Centuries) / Denise Aigle -- Western medieval specula, c. 1150-C. 1450 / Charles F. Briggs and Cary J. Nederman -- Refutation, parody, annihilation : the end of the mirror for princes in Machiavelli, Vettori and Guicciardini / Volker Reinhardt -- Specula principum and the wise governor in the Renaissance / Sylve?ne E?douard -- The influence of Aristotle's thought on Arab political-philosophical ideas / Makram Abbe?s -- The Arabic mirrors for princes as witnesses to the evolution of political thought / Makram Abbe?s -- Royal power and its regulations : narratives of Hrn al-Rashd in three mirrors for princes / Louise Marlow -- The pseudo-Aristotelian secret of secrets as a Mirror of princes : a cautionary tale / Steven J. Williams -- The Castilian versions of the pseudo-aristotle's secretum secretorum and French versions of Giles of Rome's De regimine principum (13th-16th centuries) : a comparative perspective / Hugo Bizzarri and Noe?lle-Laetitia Perret -- The relation between wisdom literature, law, and the mirrors of princes : Castile and Sweden / Olivier Biaggini and Corinne Pe?neau -- The use of mirrors of princes / Hans-Joachim Schmidt -- Conclusion : mirrors for princes and the development of reflections on the state / Jean-Philippe Genet. 330 3 $aThe literary genre collectively known as ?mirrors of princes? offers key insights into political thoughts of the past. This volume explores the genre in a global and comparative historical perspective, from antiquity to early modernity and in the Byzantine, Islamic, and Latin Christian worlds. 330 $aWhy devote a Companion to the "mirrors of princes", whose very existence is debated? These texts offer key insights into political thoughts of the past. Their ambiguous, problematic status further enhances their interest. And although recent research has fundamentally challenged established views of these texts, until now there has been no critical introduction to the genre. This volume therefore fills this important gap, while promoting a global historical perspective of different ?mirrors of princes? traditions from antiquity to humanism, via Byzantium, Persia, Islam, and the medieval West. This Companion also proposes new avenues of reflection on the anchoring of these texts in their historical realities. Contributors are Makram Abbès, Denise Aigle, Olivier Biaggini, Hugo Bizzarri, Charles F. Briggs, Sylvène Edouard, Jean-Philippe Genet, John R. Lenz, Louise Marlow, Cary J. Nederman, Corinne Peneau, Stéphane Péquignot, Noëlle-Laetitia Perret, Günter Prinzing, Volker Reinhardt, Hans-Joachim Schmidt, Tom Stevenson, Karl Ubl, and Steven J. Williams. 410 0$aReading Medieval Sources ;$v7. 606 $aCivilization$xHistory 606 $aComparative literature 607 $aByzantine Empire$xStudy and teaching 615 0$aCivilization$xHistory 615 0$aComparative literature. 676 $a940 702 $aPéquignot$b Stéphane 702 $aPerret$b Noëlle-Laetitia 801 0$bNL-LeKB 801 1$bNL-LeKB 906 $aBOOK 912 $a9910776180803321 996 $aA critical Companion to the 'Mirrors for Princes' Literature$93718324 997 $aUNINA