{"product_id":"controlled-branching-processes-hardback-9781786302533","title":"Controlled Branching Processes (Hardback) 9781786302533","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eControlled Branching Processes\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eMiguel González Velasco (Author), Inés María del Puerto García (Author), George Petrov Yanev (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781786302533, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 9 January 2018\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e232 pages\u003cbr\u003e23.6 x 16 x 1.8 cm, 0.499 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThe purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. \u003c\/p\u003e \u003cp\u003eGenerating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eForeword ix\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Classical Branching Models \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Bienaymé–Galton–Watson process 1\u003c\/p\u003e \u003cp\u003e1.1.1 Moments and probability of extinction 4\u003c\/p\u003e \u003cp\u003e1.1.2 Limit theorems 9\u003c\/p\u003e \u003cp\u003e1.2 Processes with unrestricted immigration 17\u003c\/p\u003e \u003cp\u003e1.2.1 Limit theorems 21\u003c\/p\u003e \u003cp\u003e1.2.2 Critical process with decreasing to zero immigration 25\u003c\/p\u003e \u003cp\u003e1.3 Processes with immigration after empty generation only 29\u003c\/p\u003e \u003cp\u003e1.3.1 Limit theorems 31\u003c\/p\u003e \u003cp\u003e1.3.2 Critical process with decreasing to zero immigration 36\u003c\/p\u003e \u003cp\u003e1.4 Background and bibliographical notes 40\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Branching Processes with Migration \u003c\/b\u003e\u003cb\u003e43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Galton–Watson process with migration 43\u003c\/p\u003e \u003cp\u003e2.2 Limit theorems 47\u003c\/p\u003e \u003cp\u003e2.2.1 Non-critical processes 47\u003c\/p\u003e \u003cp\u003e2.2.2 Critical processes with non-negative migration mean 49\u003c\/p\u003e \u003cp\u003e2.2.3 Critical processes with negative migration mean 52\u003c\/p\u003e \u003cp\u003e2.3 Regeneration and migration 55\u003c\/p\u003e \u003cp\u003e2.3.1 Alternating regenerative processes 56\u003c\/p\u003e \u003cp\u003e2.3.2 An extension of Galton–Watson processes with migration 58\u003c\/p\u003e \u003cp\u003e2.4 Background and bibliographical notes 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 CB Processes: Extinction \u003c\/b\u003e\u003cb\u003e65\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Definition of processes and basic properties 65\u003c\/p\u003e \u003cp\u003e3.1.1 Basic properties 69\u003c\/p\u003e \u003cp\u003e3.1.2 Probability generating functions and moments 73\u003c\/p\u003e \u003cp\u003e3.2 Extinction probability 75\u003c\/p\u003e \u003cp\u003e3.2.1 Subcritical processes 76\u003c\/p\u003e \u003cp\u003e3.2.2 Supercritical processes 78\u003c\/p\u003e \u003cp\u003e3.2.3 Critical processes 84\u003c\/p\u003e \u003cp\u003e3.3 Background and bibliographical notes 91\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 CB Processes: Limit Theorems \u003c\/b\u003e\u003cb\u003e95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Subcritical processes 95\u003c\/p\u003e \u003cp\u003e4.2 Critical processes 100\u003c\/p\u003e \u003cp\u003e4.2.1 Extinction is not certain 101\u003c\/p\u003e \u003cp\u003e4.2.2 Extinction is certain 109\u003c\/p\u003e \u003cp\u003e4.2.3 Feller diffusion approximation 110\u003c\/p\u003e \u003cp\u003e4.3 Supercritical processes 115\u003c\/p\u003e \u003cp\u003e4.3.1 Almost sure convergence 117\u003c\/p\u003e \u003cp\u003e4.3.2 L\u003csup\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/sup\u003e–convergence 118\u003c\/p\u003e \u003cp\u003e4.3.3 L\u003csup\u003e\u003cb\u003e2\u003c\/b\u003e\u003c\/sup\u003e–convergence 121\u003c\/p\u003e \u003cp\u003e4.4 Background and bibliographical notes 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Statistics of CB Processes \u003c\/b\u003e\u003cb\u003e127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Maximum likelihood estimation 127\u003c\/p\u003e \u003cp\u003e5.1.1 MLE based on entire family tree up to \u003ci\u003en\u003c\/i\u003eth generation 130\u003c\/p\u003e \u003cp\u003e5.1.2 EM algorithms for incomplete data 146\u003c\/p\u003e \u003cp\u003e5.1.3 Simulated example 152\u003c\/p\u003e \u003cp\u003e5.2 Conditional weighted least squares estimation 158\u003c\/p\u003e \u003cp\u003e5.2.1 Subcritical processes 159\u003c\/p\u003e \u003cp\u003e5.2.2 Critical processes 161\u003c\/p\u003e \u003cp\u003e5.2.3 Supercritical processes 166\u003c\/p\u003e \u003cp\u003e5.3 Minimum disparity estimation 169\u003c\/p\u003e \u003cp\u003e5.4 Bayesian inference 171\u003c\/p\u003e \u003cp\u003e5.4.1 Estimation based on entire family tree up to nth generation 172\u003c\/p\u003e \u003cp\u003e5.4.2 MCMC algorithms for incomplete data 173\u003c\/p\u003e \u003cp\u003e5.5 Background and bibliographical notes 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendices \u003c\/b\u003e\u003cb\u003e179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAppendix 1 181\u003c\/p\u003e \u003cp\u003eAppendix 2 185\u003c\/p\u003e \u003cp\u003eAppendix 3 191\u003c\/p\u003e \u003cp\u003eAppendix 4 195\u003c\/p\u003e \u003cp\u003eBibliography 197\u003c\/p\u003e \u003cp\u003eIndex 209\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-ISTE","offers":[{"title":"Brand New","offer_id":52511410422040,"sku":"9781786302533","price":100.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781786302533.jpg?v=1786599548","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/controlled-branching-processes-hardback-9781786302533","provider":"Freshly Printed Books","version":"1.0","type":"link"}