An Introduction to the Modern Martingale Theory and Applications An Analytic View /
Martingale theory is a cornerstone of modern probability, offering a natural extension of the study of sums of independent random variables. Although its roots can be traced back to the work of Paul Lévy in 1937, it was Joseph L. Doob in the 1940s who formally developed the theory, culminating in hi...
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| বিন্যাস: | বৈদ্যুতিক বৈদ্যুতিন গ্রন্থ |
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Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
|
| সংস্করন: | 1st ed. 2025. |
| মালা: | Texts in Applied Mathematics,
81 |
| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | https://doi.org/10.1007/978-3-031-88903-5 |
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| 100 | 1 | |a Urbina-Romero, Wilfredo. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 3 | |a An Introduction to the Modern Martingale Theory and Applications |h [electronic resource] : |b An Analytic View / |c by Wilfredo Urbina-Romero, Ricardo Rios. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
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| 490 | 1 | |a Texts in Applied Mathematics, |x 2196-9949 ; |v 81 | |
| 505 | 0 | |a Chapter 1: Introduction -- Chapter 2: Probability and Conditional Expectation -- Chapter 3: Advanced Topics in Martingale Theory -- Chapter 4: Burkholder’s inequalities and Davis’sinequality -- Chapter 5: Applications of Martingales. | |
| 520 | |a Martingale theory is a cornerstone of modern probability, offering a natural extension of the study of sums of independent random variables. Although its roots can be traced back to the work of Paul Lévy in 1937, it was Joseph L. Doob in the 1940s who formally developed the theory, culminating in his landmark book Stochastic Processes in 1953. Since then, martingale theory has evolved significantly, with deep contributions from mathematicians such as Donald L. Burkholder, Richard Gundy, and Burgess Davis, among others. This is what is now known as advanced martingale theory, which began with the publication of Burkholder’s seminal paper Martingale Transforms in 1966. This book provides a comprehensive treatment of both classical and advanced martingale theory. It opens with a historical introduction, exploring foundational functions such as Rademacher, Haar, and Walsh functions, before delving into the core concepts of conditional probability. The classical theory, as developed by Doob, is meticulously presented, followed by an in-depth examination of modern advancements, including Burkholder’s inequalities, Burkholder-Davis-Gundy inequality, and their generalizations, as well as good-lambda inequalities. The final chapter showcases a wide range of applications, highlighting the theory’s profound impact on Banach space theory, harmonic analysis, and beyond. Intended for graduate students and researchers in probability and analysis, this book serves as both an introduction and a reference, offering a clear and structured approach to a subject that continues to shape mathematical research and its applications. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility. It includes screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, keyboard-friendly links and forms, and searchable, selectable text. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility Please Note that a more accessible version of this eBook is available as an EPUB. | |
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