Sums of Independent Random Variables
Home > Mathematics and Science Textbooks > Mathematics > Applied mathematics > Sums of Independent Random Variables
Sums of Independent Random Variables

Sums of Independent Random Variables

|
     0     
5
4
3
2
1




Out of Stock


Notify me when this book is in stock
About the Book

Table of Contents:
I. Probability Distributions and Characteristic Functions.- 1. Random variables and probability distributions.- 2. Characteristic functions.- 3. Inversion formulae.- 4. The convergence of sequences of distributions and characteristic functions.- 5. Supplement.- II. Infinitely Divisible Distributions.- 1. Definition and elementary properties of infinitely divisible distributions.- 2. Canonical representation of infinitely divisible characteristic functions.- 3. An auxiliary theorem.- 4. Supplement.- III. Some Inequalities for the Distribution of Sums of Independent Random Variables.- 1. Concentration functions.- 2. Inequalities for the concentration functions of sums of independent random variables.- 3. Inequalities for the distribution of the maximum of sums of independent random variables.- 4. Exponential estimates for the distributions of sums of independent random variables.- 5. Supplement.- IV. Theorems on Convergence to Infinitely Divisible Distributions.- 1. Infinitely divisible distributions as limits of the distributions of sums of independent random variables.- 2. Conditions for convergence to a given infinitely divisible distribution.- 3. Limit distributions of class L and stable distributions.- 4. The central limit theorem.- 5. Supplement.- V. Estimates of the Distance Between the Distribution of a Sum of Independent Random Variables and the Normal Distribution.- 1. Estimating the nearness of functions of bounded variation by the nearness of their Fourier-Stieltjes transforms.- 2. The Esseen and Berry-Esseen inequalities.- 3. Generalizations of Esseen's inequality.- 4. Non-uniform estimates.- 5. Supplement.- VI. Asymptotic Expansions in the Central Limit Theorem.- 1. Formal construction of the expansions.- 2 Auxiliary propositions.- 3. Asymptotic expansions of the distribution function of a sum of independent identically distributed random variables.- 4. Asymptotic expansions of the distribution function of a sum of independent non-identically distributed random variables, and of the derivatives of this function.- 5. Supplement.- VII. Local Limit Theorems.- 1. Local limit theorems for lattice distributions.- 2. Local limit theorems for densities.- 3. Asymptotic expansions in local limit theorems.- 4. Supplement.- VIII. Probabilities of Large Deviations.- 1. Introduction.- 2. Asymptotic relations connected with Cramer's series.- 3. Necessary and sufficient conditions for normal convergence in power zones.- 4. Supplement.- IX. Laws of Large Numbers.- 1. The weak law of large numbers.- 2. Convergence of series of independent random variables.- 3. The strong law of large numbers.- 4. Convergence rates in the laws of large numbers.- 5. Supplement.- X. The Law of the Iterated Logarithm.- 1. Kolmogorov's theorem.- 2. Generalization of Kolmogorov's theorem.- 3. The central limit theorem and the law of the iterated logarithm.- 4. Supplement.- Notes on Sources in the Literature.- References.- Subject Indes.- Table of Symbols and Abbreviations.


Best Sellers


Product Details
  • ISBN-13: 9783540066354
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Language: English
  • Weight: 760 gr
  • ISBN-10: 3540066357
  • Publisher Date: 01 Oct 1975
  • Binding: Hardback
  • Returnable: N


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Sums of Independent Random Variables
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG -
Sums of Independent Random Variables
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Sums of Independent Random Variables

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals

    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!