Little book of martingales (Record no. 36837)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02412nam a22003137a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | NISER |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20260302172738.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 260302b |||||||| |||| 00| 0 hin d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9788195782963 |
| Qualifying information | Hardback |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | NISER LIBRARY |
| Language of cataloging | eng |
| Transcribing agency | NISER LIBRARY |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 519.216.8 |
| Item number | BOS-L |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Bose, Arup |
| 245 10 - TITLE STATEMENT | |
| Title | Little book of martingales |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | New Delhi : |
| Name of publisher, distributor, etc. | Hindustan Book Agency, |
| Date of publication, distribution, etc. | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xv, 206 pages : |
| Other physical details | illustrations ; |
| Dimensions | 24 cm. |
| 490 ## - SERIES STATEMENT | |
| Series statement | Texts and readings in mathematics ; |
| Volume/sequential designation | 86. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references and indexes. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | This little book, suitable for masters and Ph.D. programs, covers basic results on discrete time martingales and their applications. It includes some additional interesting and useful topics. Adequate details are provided, with exercises within the text and at the end of chapters.<br/><br/>Basic results include Doob's optional sampling theorem, Wald identities, Doob's maximal inequality, upcrossing lemma, time-reversed martingales, a variety of convergence results, and a limited discussion of the Burkholder inequalities. Applications include the 0-1 laws of Kolmogorov and Hewitt-Savage, the strong laws for U-statistics and for exchangeable sequences, de-Finetti's theorem for exchangeable sequences, and Kakutani's theorem for product martingales. A simple central limit theorem for martingales is proven and applied to a basic urn model, the trace of a random matrix, and Markov chains. Some of the additional topics covered are forward martingale representation for U-statistics, conditional Borel-Cantelli lemma, Azuma-Hoeffding inequality, conditional three series theorem, strong law for martingales, and the Kesten-Stigum theorem for a simple branching process.<br/><br/>A first course in measure theoretic probability is a prerequisite. We have recollected its essential concepts and results, mostly without proofs. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Martingales (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Probability theory |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Stochastic processes |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Kesten-Stigum theorem |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Radon-Nikodym theorem |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Chakrabarty, Arijit |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Hazra, Rajat Subhra |
| 856 41 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | Table of contents |
| Uniform Resource Identifier | <a href="https://www.hindbook.com/images/trim86_content.pdf">https://www.hindbook.com/images/trim86_content.pdf</a> |
| 856 41 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | Reviews |
| Uniform Resource Identifier | <a href="https://www.goodreads.com/book/show/213786398-a-little-book-of-martingales#CommunityReviews">https://www.goodreads.com/book/show/213786398-a-little-book-of-martingales#CommunityReviews</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Universal Decimal Classification |
| Koha item type | NBHM Books |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Home library | Current library | Date acquired | Total Checkouts | Full call number | Barcode | Date last seen | Price effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Universal Decimal Classification | SMS Library | SMS Library | 02/03/2026 | 519.216.8 BOS-L | N504 | 02/03/2026 | 02/03/2026 | NBHM Books |
