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Record Nr. |
UNINA9910983031903321 |
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Autore |
Henze Norbert |
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Titolo |
Very First Steps in Random Walks : The Power of Combinatorial Methods and Generating Functions / / by Norbert Henze |
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Pubbl/distr/stampa |
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Wiesbaden : , : Springer Fachmedien Wiesbaden : , : Imprint : Springer, , 2025 |
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ISBN |
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Edizione |
[1st ed. 2025.] |
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Descrizione fisica |
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1 online resource (538 pages) |
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Collana |
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Mathematics Study Resources, , 2731-3832 ; ; 17 |
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Disciplina |
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Soggetti |
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Probabilities |
Probability Theory |
Probabilitats |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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1 Introduction -- 2 The Simple Symmetric Random Walk on Z -- 3 Bridges: The Tied-down Random Walk -- 4 Asymmetric Random Walks on Z and Related Topics -- 5 Random Walks on the Integer Lattice Zd -- 6 Outlook -- 7 Tools from Stochastics, Combinatorics, and Analysis -- Solutions to the Exercises -- Bibliography. |
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Sommario/riassunto |
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With this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter. Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the |
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interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis. The Author Prof. Dr. Norbert Henze is a Professor of Stochastics at the Karlsruhe Institute of Technology (KIT), Institute of Stochastics, Karlsruhe, Germany. His well-established textbook Stochastics for Beginners (Stochastik für Einsteiger) was first published in 1997. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation. |
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