rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Probability Essentials
  name:
    name part: Jacod, Jean.
    role:
      role term: creator
  name:
    name part: Protter, Philip.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 2000
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (x, 250 pages)
  abstract: This introduction to Probability Theory can be used, at the beginning graduate level, for a one-semester course on Probability Theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as Finance Theory (Economics), Electrical Engineering, and Operations Research. The text covers the essentials in a directed and lean way with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it brings them from a starting knowledge of the subject to a knowledge of the basics of Martingale Theory. After learning Probability Theory from this text, the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.
  table of contents: Introduction -- Axioms of Probability -- Conditional Probability and Independence -- Probabilities on a Countable Space -- Random Variables on a Countable Space -- Construction of a Probability Measure -- Construction of a Probability Measure on R -- Random Variables -- Integration with Respect to a Probability Measure -- Independent Random Variables -- Probability Distributions on R -- Probability Distributions on Rn -- Characteristic Functions -- Properties of Characteristic Functions -- Sums of Independent Random Variables -- Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) -- Convergence of Random Variables; Weak Convergence -- Weak Convergence and Characteristic Functions -- The Laws of Large Numbers -- The Central Limit Theorem -- L2 and Hilbert Spaces -- Conditional Expectation -- Martingales -- Supermartingales and Submartingales -- Martingale Inequalities -- Martingale Convergence Theorems -- The Radon-Nikodym Theorem.
  note: by Jean Jacod, Philip Protter.
  note: Electronic resource.
  note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references and index.
  subject:
    topic: Mathematics
  subject:
    topic: Distribution (Probability theory)
  subject:
    topic: Probabilites
  subject:
    topic: Waarschijnlijkheidstheorie
  subject:
    topic: Probabilités
  subject:
    topic: Probabilidades
  subject:
    topic: Wahrscheinlichkeitstheorie
  subject:
    topic: Distribution (Probability theory)
  subject:
    topic: Mathematics
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  classification: 31.70
  classification: MAT 600f
  classification: QH 170
  classification: SK 800
  related item:
    title info:
      title: Universitext
  identifier: 9783642514319 (electronic bk.)
  identifier: 3642514316 (electronic bk.)
  identifier: 9783540664192
  identifier: 354066419X
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 121227
    record change date: 20260422154508.8
    record identifier: in00003576992
    language of cataloging:
      language term: eng