From Measures to Itô Integrals /:
"From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure th...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2011, ©2011.
|
| Schriftenreihe: | AIMS library series.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus"-- "Undergraduate mathematics syllabi vary considerably in their coverage of measure-theoretic probability theory, so beginning graduates often find substantial gaps in their background when attending modules in advanced analysis, stochastic processes and applications. This text seeks to fill some of these gaps concisely. The exercises form an integral part of the text. The material arose from my experience of teaching AIMS students between 2004 and 2007, of which I retain many fond memories. The AIMS series format allows few explorations of byways; and the objective of arriving at a reasonably honest but concise account of the Itô integral decided most of the material. With motivation from elementary probability we discuss measures and integrals, leading via L2-theory and conditional expectation to discrete martingales and an outline proof of the Radon-Nikodym Theorem. The last two chapters introduce Brownian Motion and Itô integrals, with a brief look at martingale calculus. Here proofs of several key results are only sketched briefly or omitted. The Black-Scholes option pricing model provides the main application. None of the results presented is new; any remaining errors are mine"-- |
| Beschreibung: | 1 online resource (vii, 120 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (page 118) and index. |
| ISBN: | 9781139078870 1139078879 9781139081146 1139081144 9780511813115 0511813112 9781139083416 1139083414 |
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| 520 | |a "From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus"-- |c Provided by publisher. | ||
| 520 | |a "Undergraduate mathematics syllabi vary considerably in their coverage of measure-theoretic probability theory, so beginning graduates often find substantial gaps in their background when attending modules in advanced analysis, stochastic processes and applications. This text seeks to fill some of these gaps concisely. The exercises form an integral part of the text. The material arose from my experience of teaching AIMS students between 2004 and 2007, of which I retain many fond memories. The AIMS series format allows few explorations of byways; and the objective of arriving at a reasonably honest but concise account of the Itô integral decided most of the material. With motivation from elementary probability we discuss measures and integrals, leading via L2-theory and conditional expectation to discrete martingales and an outline proof of the Radon-Nikodym Theorem. The last two chapters introduce Brownian Motion and Itô integrals, with a brief look at martingale calculus. Here proofs of several key results are only sketched briefly or omitted. The Black-Scholes option pricing model provides the main application. None of the results presented is new; any remaining errors are mine"-- |c Provided by publisher. | ||
| 504 | |a Includes bibliographical references (page 118) and index. | ||
| 505 | 0 | |a Probability and measure -- Measures and distribution functions -- Measurable functions/random variables -- Integration and expectation -- Lp-spaces and conditional expectation -- Discrete-time martingales -- Brownian motion -- Stochastic integrals. | |
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| contents | Probability and measure -- Measures and distribution functions -- Measurable functions/random variables -- Integration and expectation -- Lp-spaces and conditional expectation -- Discrete-time martingales -- Brownian motion -- Stochastic integrals. |
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| indexdate | 2024-11-27T13:17:49Z |
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| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (vii, 120 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | AIMS library series. |
| series2 | African Institute of Mathematics Library Series |
| spelling | Kopp, P. E., 1944- author. https://id.oclc.org/worldcat/entity/E39PBJxrVdrPwWKR39tDPq9Rrq http://id.loc.gov/authorities/names/n83133988 From Measures to Itô Integrals / Ekkehard Kopp. Cambridge ; New York : Cambridge University Press, 2011, ©2011. 1 online resource (vii, 120 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier African Institute of Mathematics Library Series "From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus"-- Provided by publisher. "Undergraduate mathematics syllabi vary considerably in their coverage of measure-theoretic probability theory, so beginning graduates often find substantial gaps in their background when attending modules in advanced analysis, stochastic processes and applications. This text seeks to fill some of these gaps concisely. The exercises form an integral part of the text. The material arose from my experience of teaching AIMS students between 2004 and 2007, of which I retain many fond memories. The AIMS series format allows few explorations of byways; and the objective of arriving at a reasonably honest but concise account of the Itô integral decided most of the material. With motivation from elementary probability we discuss measures and integrals, leading via L2-theory and conditional expectation to discrete martingales and an outline proof of the Radon-Nikodym Theorem. The last two chapters introduce Brownian Motion and Itô integrals, with a brief look at martingale calculus. Here proofs of several key results are only sketched briefly or omitted. The Black-Scholes option pricing model provides the main application. None of the results presented is new; any remaining errors are mine"-- Provided by publisher. Includes bibliographical references (page 118) and index. Probability and measure -- Measures and distribution functions -- Measurable functions/random variables -- Integration and expectation -- Lp-spaces and conditional expectation -- Discrete-time martingales -- Brownian motion -- Stochastic integrals. Print version record. Measure theory Textbooks. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Calculus. bisacsh Medición embne Measure theory fast Maßtheorie gnd Electronic book. Textbooks fast has work: From Measures to Itô Integrals (Text) https://id.oclc.org/worldcat/entity/E39PCGVFbxQqRryBtbcQgXX3cd https://id.oclc.org/worldcat/ontology/hasWork Print version: Kopp, Ekkehard (Peter Ekkehard), 1944- From Measures to Itô Integrals. Cambridge ; New York : Cambridge University Press, 2011, ©2011 9781107400863 (DLC) 2010050362 (OCoLC)690090166 AIMS library series. http://id.loc.gov/authorities/names/no2010112645 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=366254 Volltext |
| spellingShingle | Kopp, P. E., 1944- From Measures to Itô Integrals / AIMS library series. Probability and measure -- Measures and distribution functions -- Measurable functions/random variables -- Integration and expectation -- Lp-spaces and conditional expectation -- Discrete-time martingales -- Brownian motion -- Stochastic integrals. Measure theory Textbooks. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Calculus. bisacsh Medición embne Measure theory fast Maßtheorie gnd |
| title | From Measures to Itô Integrals / |
| title_auth | From Measures to Itô Integrals / |
| title_exact_search | From Measures to Itô Integrals / |
| title_full | From Measures to Itô Integrals / Ekkehard Kopp. |
| title_fullStr | From Measures to Itô Integrals / Ekkehard Kopp. |
| title_full_unstemmed | From Measures to Itô Integrals / Ekkehard Kopp. |
| title_short | From Measures to Itô Integrals / |
| title_sort | from measures to ito integrals |
| topic | Measure theory Textbooks. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Calculus. bisacsh Medición embne Measure theory fast Maßtheorie gnd |
| topic_facet | Measure theory Textbooks. MATHEMATICS Mathematical Analysis. MATHEMATICS Calculus. Medición Measure theory Maßtheorie Electronic book. Textbooks |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=366254 |
| work_keys_str_mv | AT kopppe frommeasurestoitointegrals |