Author | Loรจve, M. author |
---|---|

Title | Probability Theory I [electronic resource] / by M. Loรจve |

Imprint | New York, NY : Springer New York, 1977 |

Edition | 4th Edition |

Connect to | http://dx.doi.org/10.1007/978-1-4684-9464-8 |

Descript | XVIII, 428 p. online resource |

SUMMARY

This fourth edition contains several additions. The main ones conยญ cern three closely related topics: Brownian motion, functional limit distributions, and random walks. Besides the power and ingenuity of their methods and the depth and beauty of their results, their importance is fast growing in Analysis as well as in theoretical and applied Probaยญ bility. These additions increased the book to an unwieldy size and it had to be split into two volumes. About half of the first volume is devoted to an elementary introducยญ tion, then to mathematical foundations and basic probability concepts and tools. The second half is devoted to a detailed study of Independยญ ence which played and continues to playa central role both by itself and as a catalyst. The main additions consist of a section on convergence of probabilities on metric spaces and a chapter whose first section on domains of attracยญ tion completes the study of the Central limit problem, while the second one is devoted to random walks. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated. The main addition consists of a chapter on Brownian motion and limit distributions

CONTENT

of Volume I -- Introductory Part: Elementary Probability Theory -- I. Intuitive Background -- II. Axioms; Independence and the Bernoulli Case -- III. Dependence and Chains -- Complements and Details -- One: Notions of Measure Theory -- I: Sets, Spaces, and Measures -- II: Measurable Functions and Integration -- Two: General Concepts and Tools of Probability Theory -- III: Probability Concepts -- IV: Distribution Functions and Characteristic Functions -- Three: Independence -- V: Sums of Independent Random Variables -- VI: Central Limit Problem -- VII: Independent Identically Distributed Summands

Mathematics
Probabilities
Mathematics
Probability Theory and Stochastic Processes