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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Physical Description: | 1 online resource (130 pages) |
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Löffler, Andreas. The Brownian Motion : A Rigorous but Gentle Introduction for Economists. 1st ed. Cham : Springer International Publishing AG, 2019. {copy}2019. 1 online resource (130 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Springer Texts in Business and Economics Series 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. Description based on publisher supplied metadata and other sources. Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. Electronic books. Kruschwitz, Lutz. Print version: Löffler, Andreas The Brownian Motion Cham : Springer International Publishing AG,c2019 9783030201029 ProQuest (Firm) https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=5917773 Click to View |
language |
English |
format |
eBook |
author |
Löffler, Andreas. |
spellingShingle |
Löffler, Andreas. The Brownian Motion : A Rigorous but Gentle Introduction for Economists. Springer Texts in Business and Economics Series 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. |
author_facet |
Löffler, Andreas. Kruschwitz, Lutz. |
author_variant |
a l al |
author2 |
Kruschwitz, Lutz. |
author2_variant |
l k lk |
author2_role |
TeilnehmendeR |
author_sort |
Löffler, Andreas. |
title |
The Brownian Motion : A Rigorous but Gentle Introduction for Economists. |
title_sub |
A Rigorous but Gentle Introduction for Economists. |
title_full |
The Brownian Motion : A Rigorous but Gentle Introduction for Economists. |
title_fullStr |
The Brownian Motion : A Rigorous but Gentle Introduction for Economists. |
title_full_unstemmed |
The Brownian Motion : A Rigorous but Gentle Introduction for Economists. |
title_auth |
The Brownian Motion : A Rigorous but Gentle Introduction for Economists. |
title_new |
The Brownian Motion : |
title_sort |
the brownian motion : a rigorous but gentle introduction for economists. |
series |
Springer Texts in Business and Economics Series |
series2 |
Springer Texts in Business and Economics Series |
publisher |
Springer International Publishing AG, |
publishDate |
2019 |
physical |
1 online resource (130 pages) |
edition |
1st ed. |
contents |
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. |
isbn |
9783030201036 9783030201029 |
callnumber-first |
H - Social Science |
callnumber-subject |
HG - Finance |
callnumber-label |
HG1-9999 |
callnumber-sort |
HG 11 49999 |
genre |
Electronic books. |
genre_facet |
Electronic books. |
url |
https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=5917773 |
illustrated |
Not Illustrated |
oclc_num |
1110741362 |
work_keys_str_mv |
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hierarchy_parent_title |
Springer Texts in Business and Economics Series |
is_hierarchy_title |
The Brownian Motion : A Rigorous but Gentle Introduction for Economists. |
container_title |
Springer Texts in Business and Economics Series |
author2_original_writing_str_mv |
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