The Brownian Motion : : A Rigorous but Gentle Introduction for Economists.
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Superior document: | Springer Texts in Business and Economics Series |
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Place / Publishing House: | Cham : : Springer International Publishing AG,, 2019. {copy}2019. |
Year of Publication: | 2019 |
Edition: | 1st ed. |
Language: | English |
Series: | Springer Texts in Business and Economics Series
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Online Access: | |
Physical Description: | 1 online resource (130 pages) |
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100 | 1 | |a Löffler, Andreas. | |
245 | 1 | 4 | |a The Brownian Motion : |b A Rigorous but Gentle Introduction for Economists. |
250 | |a 1st ed. | ||
264 | 1 | |a Cham : |b Springer International Publishing AG, |c 2019. | |
264 | 4 | |c {copy}2019. | |
300 | |a 1 online resource (130 pages) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
490 | 1 | |a Springer Texts in Business and Economics Series | |
505 | 0 | |a Intro -- Preface -- Acknowledgments -- Contents -- 1 Introduction -- 1.1 Stochastics in Finance Theory -- 1.2 Precision and Intuition in the Valuation of Derivatives -- 1.3 Purpose of the Book -- 2 Set Theory -- 2.1 Notation and Set Operations -- 2.2 Events and Sets -- 3 Measures and Probabilities -- 3.1 Basic Problem of Measurement Theory -- 3.2 σ-Algebras and Their Formal Definition -- 3.3 Examples of Measurable Sets and Their Interpretation -- 3.4 Further Examples: Infinite Number of States and Times -- 3.5 Definition of a Measure -- 3.6 Stieltjes Measure -- 3.7 Dirac Measure -- 3.8 Null Sets and the Almost-Everywhere Property -- 4 Random Variables -- 4.1 Random Variables as Functions -- 4.2 Random Variables as Measurable Functions -- 4.3 Distribution Functions -- 5 Expectation and Lebesgue Integral -- 5.1 Definition of Expectation: A Problem -- 5.2 Riemann Integral -- 5.3 Lebesgue Integral -- 5.4 Result: Expectation and Variance as Lebesgue Integral -- 5.5 Conditional Expectation -- 6 Wiener's Construction of the Brownian Motion -- 6.1 Preliminary Remark: The Space of All Paths -- 6.2 Wiener Measure on the Space of Continuous Functions -- 6.3 Two Definitions of the Brownian Motion -- 6.4 Often Neglected Properties of the Brownian Motion -- 7 Supplements -- 7.1 Cardinality of Sets -- 7.2 Continuous and Almost Nowhere Differentiable Functions -- 7.3 Convergence Terms -- 7.4 Conditional Expectations Are Random Variables -- References -- Index. | |
588 | |a Description based on publisher supplied metadata and other sources. | ||
590 | |a Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. | ||
655 | 4 | |a Electronic books. | |
700 | 1 | |a Kruschwitz, Lutz. | |
776 | 0 | 8 | |i Print version: |a Löffler, Andreas |t The Brownian Motion |d Cham : Springer International Publishing AG,c2019 |z 9783030201029 |
797 | 2 | |a ProQuest (Firm) | |
830 | 0 | |a Springer Texts in Business and Economics Series | |
856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=5917773 |z Click to View |