{"product_id":"markov-chains-with-asymptotically-zero-drift-lampertis-problem-hardback-9781009554220","title":"Markov Chains with Asymptotically Zero Drift; Lamperti's Problem (Hardback) 9781009554220","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eMarkov Chains with Asymptotically Zero Drift\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eLamperti's Problem\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eA comprehensive presentation of results for time-homogeneous Markov chains with asymptotically zero drift.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDenis Denisov (Author), Dmitry Korshunov (Author), Vitali Wachtel (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009554220, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 8 May 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e428 pages\u003cbr\u003e23.5 x 15.8 x 2.3 cm, 0.76 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\"\u003eThis text examines Markov chains whose drift tends to zero at infinity, a topic sometimes labelled as 'Lamperti's problem'. It can be considered a subcategory of random walks, which are helpful in studying stochastic models like branching processes and queueing systems. Drawing on Doob's h-transform and other tools, the authors present novel results and techniques, including a change-of-measure technique for near-critical Markov chains. The final chapter presents a range of applications where these special types of Markov chains occur naturally, featuring a new risk process with surplus-dependent premium rate. This will be a valuable resource for researchers and graduate students working in probability theory and stochastic processes.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. Lyapunov functions and classification of Markov chains\u003cbr\u003e 3. Down-crossing probabilities for transient Markov chain\u003cbr\u003e 4. Limit theorems for transient and null-recurrent Markov chains with drift proportional to 1\/x\u003cbr\u003e 5. Limit theorems for transient Markov chains with drift decreasing slower than 1\/x\u003cbr\u003e 6. Asymptotics for renewal measure for transient Markov chain via martingale approach\u003cbr\u003e 7. Doob's h-transform: transition from recurrent to transient chain and vice versa\u003cbr\u003e 8. Tail analysis for recurrent Markov chains with drift proportional to 1\/x\u003cbr\u003e 9. Tail analysis for positive recurrent Markov chains with drift going to zero slower than 1\/x\u003cbr\u003e 10. Markov chains with asymptotically non-zero drift in Cramér's case\u003cbr\u003e 11. Applications.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52509158277400,"sku":"9781009554220","price":96.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009554220i.jpg?v=1786494786","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/markov-chains-with-asymptotically-zero-drift-lampertis-problem-hardback-9781009554220","provider":"Freshly Printed Books","version":"1.0","type":"link"}