MTU Cork Library Catalogue

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Counterexamples in probability / Iordan Stoianov.

By: Stoianov, Iordan.
Material type: materialTypeLabelBookPublisher: England : Wiley, c1987Description: xxiii, 313 p. ; 23 cm. + hbk.ISBN: 0471916498.Subject(s): ProbabilitiesDDC classification: 519.2
Contents:
Classes of random events -- Probabilities -- Independence of random events -- Diverse properties of random events and their probabilities -- Distribution functions of random variables -- Expectations and conditional expectations -- Independence of random variables -- Characteristic and generating functions -- Infinitely divisible and stable distributions -- Normal distributions -- The moment problem -- Characterization properties of some probability distributions -- Diverse properties of random variables -- Various kinds of convergence of sequences of random variables -- Laws of large numbers -- Weak convergence of probability measures and distributions -- Central limit theorem -- Diverse limit theorems -- Basic notions of Stochastic processes -- Markov processes -- Stationary processes and some related topics -- Discrete time martingales -- Continuous time martingales -- Poisson process and Weiner process -- Diverse properties of Stochastic prosesses.
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
General Lending MTU Bishopstown Library Lending 519.2 (Browse shelf(Opens below)) 1 Available 00030595
Total holds: 0

Enhanced descriptions from Syndetics:

Counterexamples (in the usual mathematical sense) are powerful tools of mathematical theory. In this book the author gives more than 250 drawn from the whole field of probability theory and stochastic processes. The counterexamples are selected for their interest and for the importance of the theory they illustrate. Each section starts with a summary of definitions and main results, followed by counterexamples ordered by content and difficulty. Full references and additional sources are given.

Classes of random events -- Probabilities -- Independence of random events -- Diverse properties of random events and their probabilities -- Distribution functions of random variables -- Expectations and conditional expectations -- Independence of random variables -- Characteristic and generating functions -- Infinitely divisible and stable distributions -- Normal distributions -- The moment problem -- Characterization properties of some probability distributions -- Diverse properties of random variables -- Various kinds of convergence of sequences of random variables -- Laws of large numbers -- Weak convergence of probability measures and distributions -- Central limit theorem -- Diverse limit theorems -- Basic notions of Stochastic processes -- Markov processes -- Stationary processes and some related topics -- Discrete time martingales -- Continuous time martingales -- Poisson process and Weiner process -- Diverse properties of Stochastic prosesses.

Table of contents provided by Syndetics

  • Classes Of Random Events And Probabilities
  • Classes of Random Events
  • Independence of Random Events
  • Random Variables And Basic Characteristics
  • Distribution Functions of Random Variables
  • Expectations and Conditional Expectations
  • Characteristic and Generating Functions
  • Infinitely Divisible and Stable Distributions
  • The Moment Problem
  • Diverse Properties of Random Variables
  • Limit Theorems
  • Laws of Large Numbers
  • Weak Convergence of Probability Measures and Distributions
  • STochastic Processes
  • Basic Notions on Stochastic Processes
  • Markov Processes
  • Poisson Process and Wiener Process
  • Supplementary Remarks
  • References
  • Index

Reviews provided by Syndetics

CHOICE Review

For the creation of this very well written and thorough book Stoyanov possesses an exceptional background in probability theory and stochastic processes; he also provides input from other knowledgeable mathematicians around the world. The author offers more than 250 counterexamples from probability theory and stochastic processes; these range over various degrees of difficulty and it is assumed that the reader is familiar with both topics. The book is very effectively organized; each section has introductory notes with basic definitions and main results, and also counterexamples related to these results. The main themes developed are random events and their probabilities, random variables, distributions and major characteristics, limit theorems, and stochastic processes. References give necessary and very helpful background information on the subject. Depending on the sections covered, the book may be appropriate for an undergraduate or graduate course in probability if the student is familiar with measure theory and function theory. Highly recommended for both undergraduate and graduate libraries. -D. J. Gougeon, University of Scranton

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