LEADER 03456nam 22005415 450 001 9910983031903321 005 20251106094535.0 010 $a9783658463137 010 $a3658463139 024 7 $a10.1007/978-3-658-46313-7 035 $a(CKB)37516353500041 035 $a(MiAaPQ)EBC31921678 035 $a(Au-PeEL)EBL31921678 035 $a(DE-He213)978-3-658-46313-7 035 $a(OCoLC)1503845054 035 $a(EXLCZ)9937516353500041 100 $a20250212d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aVery First Steps in Random Walks $eThe Power of Combinatorial Methods and Generating Functions /$fby Norbert Henze 205 $a1st ed. 2025. 210 1$aWiesbaden :$cSpringer Fachmedien Wiesbaden :$cImprint: Springer,$d2025. 215 $a1 online resource (538 pages) 225 1 $aMathematics Study Resources,$x2731-3832 ;$v17 311 08$a9783658463120 311 08$a3658463120 327 $a1 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. 330 $aWith this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter. Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis. The Author Prof. Dr. Norbert Henze is a Professor of Stochastics at the Karlsruhe Institute of Technology (KIT), Institute of Stochastics, Karlsruhe, Germany. His well-established textbook Stochastics for Beginners (Stochastik für Einsteiger) was first published in 1997. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation. 410 0$aMathematics Study Resources,$x2731-3832 ;$v17 606 $aProbabilities 606 $aProbability Theory 606 $aProbabilitats$2thub 608 $aLlibres electrònics$2thub 615 0$aProbabilities. 615 14$aProbability Theory. 615 7$aProbabilitats 676 $a519.2 700 $aHenze$b Norbert$01229276 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910983031903321 996 $aVery First Steps in Random Walks$94316978 997 $aUNINA