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Anomalous Stochastics : A Comprehensive Guide to Multifractals, Random Walks, and Real-World Applications / by Michał Chorowski, Tomasz Gubiec, Ryszard Kutner

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Understanding Complex SystemsPublisher: Cham : Springer Nature Switzerland, 2025Edition: 1st ed. 2025Description: 1 Online-Ressource(XV, 402 p. 70 illus., 16 illus. in color.)ISBN:
  • 9783031803925
Subject(s): Additional physical formats: 9783031803918 | 9783031803932 | 9783031803949 | Erscheint auch als: 9783031803918 Druck-Ausgabe | Erscheint auch als: 9783031803932 Druck-Ausgabe | Erscheint auch als: 9783031803949 Druck-Ausgabe | Erscheint auch als: Anomalous stochastics. Druck-Ausgabe Cham : Springer Nature Switzerland, 2025. xv, 402 SeitenDDC classification:
  • 519.23 23
DOI: DOI: 10.1007/978-3-031-80392-5Online resources: Summary: Introduction -- Fundamental Concepts -- Singular Stochastic Processes -- Non-deterministic Fractals -- Signatures and Causes of Multifractality -- Dispersive Transport and Diffusion -- Fractal Wanderings -- Valley Model of Multifractal Continuous-time Random Wandering on Amorphous Substrates -- Statistics of Extremes -- Limit Theorems on the Stock Market -- Comprehensive Partition Function: A Universal Tool in Multifractality.Summary: This textbook provides a comprehensive exploration of anomalous stochastic processes and extreme events, commonly referred to as "black swans," with a particular focus on (multi-)fractal approaches and continuous-time random walks. The authors present a systematic examination of the subject, tracing its inception and providing a multi-directional perspective. By drawing on real-world experiences in finance, physics, and technology, the book underscores the practical relevance of anomalous stochastic processes for practitioners dealing with real-world data from complex systems. The content is based on a series of interdisciplinary physics lectures that have been delivered to undergraduate and graduate students at the University of Warsaw for nearly two decades. Updated to reflect recent developments, this book is a valuable resource for graduate students, ambitious undergraduate students, and researchers interested in random processes and the practical implications of anomalous processes. Familiarity with fundamental principles of probability theory, algebra, and basic concepts of differential and integral calculus is assumed, while a foundational understanding of mathematical statistics, stochastic processes, and statistical thermodynamics is recommended. Additionally, each chapter includes practical exercises designed to help readers master the concepts, develop practical skills, and serve as teaching material.PPN: PPN: 1921824514Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-PHA | ZDB-2-SXP
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