001450487 000__ 06835cam\a2200589\i\4500
001450487 001__ 1450487
001450487 003__ OCoLC
001450487 005__ 20230310004528.0
001450487 006__ m\\\\\o\\d\\\\\\\\
001450487 007__ cr\cn\nnnunnun
001450487 008__ 221021s2022\\\\sz\a\\\\o\\\\\001\0\eng\d
001450487 019__ $$a1348492805
001450487 020__ $$a9783031059889$$q(electronic bk.)
001450487 020__ $$a3031059883$$q(electronic bk.)
001450487 020__ $$z9783031059872
001450487 020__ $$z3031059875
001450487 0247_ $$a10.1007/978-3-031-05988-9$$2doi
001450487 035__ $$aSP(OCoLC)1348287402
001450487 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCF$$dOCLCQ
001450487 049__ $$aISEA
001450487 050_4 $$aQA274.5
001450487 08204 $$a519.2/87$$223/eng/20221031
001450487 24504 $$aThe splendors and miseries of martingales :$$btheir history from the casino to mathematics /$$cLaurent Mazliak, Glenn Shafer, editors.
001450487 264_1 $$aCham :$$bBirkhäuser,$$c[2022]
001450487 264_4 $$c©2022
001450487 300__ $$a1 online resource (xiv, 418 pages) :$$billustrations (some color).
001450487 336__ $$atext$$btxt$$2rdacontent
001450487 337__ $$acomputer$$bc$$2rdamedia
001450487 338__ $$aonline resource$$bcr$$2rdacarrier
001450487 4901_ $$aTrends in the history of science
001450487 500__ $$aIncludes index.
001450487 5050_ $$aIntro -- Introduction -- Contents -- Part I In the Beginning -- 1 The Origin and Multiple Meanings of Martingale -- 1 Introduction -- 2 From Probability Back to Gambling -- 3 Are Martingales Foolish? -- 4 An Excursion Around Martigues -- 5 Back to Harnesses -- 6 The Ultimate Treachery of Martingales -- 2 Martingales at the Casino -- 1 Prelude -- 2 Introduction -- 3 The Casino -- 3.1 Trente et Quarante -- 3.2 The Business Model -- 3.3 The Paris Casinos -- 4 Gamblers' Fallacies -- 4.1 Two Moralists -- 4.2 The Blatant Rogue -- 4.3 The Failed Mathematician -- 4.4 The Many-Talented Gambler
001450487 5058_ $$a5 Betting Systems and Game Theory -- 3 Émile Borel's Denumerable Martingales, 1909-1949 -- 1 Introduction -- 2 Martingales of Fathers of Families -- 3 Borel's Martingales -- 4 The Dawn of Martingale Convergence: Jessen's Theorem and Lévy's Lemma -- 1 Introduction -- 2 Jessen's Theorem -- 2.1 Magister Thesis 1929 -- 2.2 Doctoral Thesis 1930 -- 2.3 The Acta Article 1934 -- 2.4 A Probabilistic Interlude 1934-1935 -- 2.5 After 1934 -- 3 Lévy's Lemma -- 3.1 Before 1930 -- 3.2 Lévy's Denumerable Probabilities -- *-20pt Part II Ville, Lévy and Doob -- 5 Did Jean Ville Invent Martingales?
001450487 5058_ $$a1 Introduction -- 2 A Glimpse of Jean Ville -- 3 Probability as Ville Encountered It in the Early 1930s -- 4 Martingales in Probability Before Ville -- 5 Combining Game Theory with Denumerable Probability -- 6 Legacy -- 7 A Final Question -- 6 Paul Lévy's Perspective on Jean Ville and Martingales -- 1 Introduction -- 2 Lévy and His Martingale Condition -- 2.1 Lévy's Growing Interest in Probability -- 2.2 Genesis of Lévy's Martingale Condition -- 2.3 Chapter VIII of the Book Théorie de l'addition des variables aléatoires -- 3 Lévy Versus Ville -- 4 Conclusion
001450487 5058_ $$a7 Doob at Lyon: Bringing Martingales Back to France -- 1 The Colloquium -- 2 Paul Lévy -- 3 Jean Ville -- 4 Joseph Doob -- 5 At the Colloquium -- 6 Doob's Lecture -- 6.1 Strong Law of Large Numbers -- 6.2 Inverse Probability -- *-20pt Part III Modern Probability -- 8 Stochastic Processes in the Decades after 1950 -- 1 Introduction -- 2 Probability Around 1950 -- 2.1 Early Developments -- 2.2 ``Stochastic Processes'' -- 3 The Great Topics of the Years 1950-1965 -- 3.1 Markov Processes -- 3.2 Development of Soviet Probability -- 3.3 Classical Potential Theory and Probability
001450487 5058_ $$a3.4 Theory of Martingales -- 3.5 Markov Processes and Potential -- 3.6 Special Markov Processes -- 3.7 Connections Between Markov Processes and Martingales -- 4 The Period 1965-1980 -- 4.1 The Stochastic Integral -- 4.2 Markov Processes -- 4.3 General Theory of Processes -- 4.4 Inequalities of Martingales and Analysis -- 4.5 Martingale Problems -- 4.6 ``Stochastic Mechanics'' -- 4.7 Relations to Physics -- 5 After 1980 -- 5.1 The ``Malliavin Calculus'' -- 5.2 Stochastic Differential Geometry -- 5.3 Distributions and White Noise -- 5.4 Large Deviations -- 5.5 Noncommutative Probability
001450487 506__ $$aAccess limited to authorized users.
001450487 520__ $$aOver the past eighty years, martingales have become central in the mathematics of randomness. They appear in the general theory of stochastic processes, in the algorithmic theory of randomness, and in some branches of mathematical statistics. Yet little has been written about the history of this evolution. This book explores some of the territory that the history of the concept of martingales has transformed. The historian of martingales faces an immense task. We can find traces of martingale thinking at the very beginning of probability theory, because this theory was related to gambling, and the evolution of a gamblers holdings as a result of following a particular strategy can always be understood as a martingale. More recently, in the second half of the twentieth century, martingales became important in the theory of stochastic processes at the very same time that stochastic processes were becoming increasingly important in probability, statistics and more generally in various applied situations. Moreover, a history of martingales, like a history of any other branch of mathematics, must go far beyond an account of mathematical ideas and techniques. It must explore the context in which the evolution of ideas took place: the broader intellectual milieux of the actors, the networks that already existed or were created by the research, even the social and political conditions that favored or hampered the circulation and adoption of certain ideas. This books presents a stroll through this history, in part a guided tour, in part a random walk. First, historical studies on the period from 1920 to 1950 are presented, when martingales emerged as a distinct mathematical concept. Then insights on the period from 1950 into the 1980s are offered, when the concept showed its value in stochastic processes, mathematical statistics, algorithmic randomness and various applications.
001450487 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 31, 2022).
001450487 650_0 $$aMartingales (Mathematics)$$xHistory.
001450487 655_7 $$aHistory.$$2fast$$0(OCoLC)fst01411628
001450487 655_0 $$aElectronic books.
001450487 7001_ $$aMazliak, Laurent,$$eeditor.
001450487 7001_ $$aShafer, Glenn,$$d1946-$$eeditor.
001450487 77608 $$iPrint version: $$z3031059875$$z9783031059872$$w(OCoLC)1310623025
001450487 830_0 $$aTrends in the history of science.
001450487 852__ $$bebk
001450487 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-05988-9$$zOnline Access$$91397441.1
001450487 909CO $$ooai:library.usi.edu:1450487$$pGLOBAL_SET
001450487 980__ $$aBIB
001450487 980__ $$aEBOOK
001450487 982__ $$aEbook
001450487 983__ $$aOnline
001450487 994__ $$a92$$bISE