Probability Theory : Independence Interchangeability Martingales

Yuan Shih Chow

ISBN 10: 1468400649 / ISBN 13: 9781468400649

Edité par Springer Feb 2012, 2012

A propos de cet article

Neuware - Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub- ject, generally attributed to investigations by the renowned french mathe- matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure- theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment which is at least conceptually capable of indefi- nite repetition (this notion is due to von Mises). The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome.

N° de réf. du vendeur 9781468400649

Détails bibliographiques

• Titre: Probability Theory : Independence Interchangeability Martingales
• Éditeur: Springer Feb 2012
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 1468400649
• ISBN à 13 chiffres: 9781468400649
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 234 L x 156 H x 25 P (en millimètres) 234 millimètres de largeur par 156 millimètres de hauteur par 25 millimètres de profondeur
• Poids: 667 grammes

A propos de ce titre

Synopsis

Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub- ject, generally attributed to investigations by the renowned french mathe- matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure- theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment which is at least conceptually capable of indefi- nite repetition (this notion is due to von Mises). The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome.