{"product_id":"compound-renewal-processes-hardback-9781009098441","title":"Compound Renewal Processes (Hardback) 9781009098441","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eCompound Renewal Processes\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThe first unified presentation of the general asymptotic theory of compound renewal processes, with classical and functional limit theorems.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eA. A. Borovkov (Author), Alexey Alimov (Translated by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009098441, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 June 2022\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e379 pages\u003cbr\u003e24.1 x 16.5 x 2.1 cm, 0.7 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\"\u003eCompound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. Main limit laws in the normal deviation zone\u003cbr\u003e 2. Integro-local limit theorems in the normal deviation zone\u003cbr\u003e 3. Large deviation principles for compound renewal processes\u003cbr\u003e 4. Large deviation principles for trajectories of compound renewal processes\u003cbr\u003e 5. Integro-local limit theorems under the Cramér moment condition\u003cbr\u003e 6. Exact asymptotics in boundary crossing problems for compound renewal processes\u003cbr\u003e 7. Extension of the invariance principle to the zones of moderately large and small deviations\u003cbr\u003e A. On boundary crossing problems for compound renewal processes when the Cramér condition is not fulfilled\u003cbr\u003e Basic notation\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Stochastics [\u003ca title=\"See our other books on Stochastics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Stochastics%20%5BPBWL%5D%22\"\u003ePBWL\u003c\/a\u003e], Mathematical modelling [\u003ca title=\"See our other books on Mathematical modelling\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20modelling%20%5BPBWH%5D%22\"\u003ePBWH\u003c\/a\u003e], 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], Information theory [\u003ca title=\"See our other books on Information theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Information%20theory%20%5BGPF%5D%22\"\u003eGPF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265387155736,"sku":"9781009098441","price":93.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781009098441i_9bf3fdc9-09d7-42a6-8581-b7e5e9f42414.jpg?v=1696791169","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/compound-renewal-processes-hardback-9781009098441","provider":"Freshly Printed Books","version":"1.0","type":"link"}