{"product_id":"9783030015251","title":"Probability Theory and Stochastic Modelling","description":"\u003ch1\u003eProbability Theory and Stochastic Modelling\u003c\/h1\u003e \u003ch2\u003eShiryaev, Albert N.; Poor, H. Vincent; Iacob, Andrei\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis monograph focuses on those stochastic \u003ci\u003equickest detection tasks \u003c\/i\u003ein disorder problems that arise in the dynamical analysis of statistical data. These include quickest detection of randomly appearing targets, of spontaneously arising effects, and of arbitrage (in financial mathematics). There is also currently great interest in quickest detection methods for randomly occurring intrusions in information systems and in the design of defense methods against cyber-attacks. The author shows that the majority of quickest detection problems can be reformulated as \u003ci\u003eoptimal stopping problems\u003c\/i\u003e where the stopping time is the moment the occurrence of disorder is signaled. Thus, considerable attention is devoted to the general theory of optimal stopping rules, and to its concrete problem-solving methods.\u003c\/p\u003e\u003cp\u003eThe exposition covers both the \u003ci\u003ediscrete time \u003c\/i\u003ecase, which is in principle relatively simple and allows step-by-step considerations, and the \u003ci\u003econtinuous-time case\u003c\/i\u003e,\u003ci\u003e \u003c\/i\u003ewhich\u003ci\u003e \u003c\/i\u003eoften requires more technical machinery such as martingales, supermartingales, and stochastic integrals. There is a focus on the well-developed apparatus of Brownian motion, which enables the exact solution of many problems. The last chapter presents applications to financial markets.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eResearchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2019-03-20\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030015251\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-01526-8\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 397\u003c\/p\u003e ","brand":"Moscow Center for Continuous Mathematical Education","offers":[{"title":"Default Title","offer_id":44807408517260,"sku":"9783030015251","price":125.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030015251.jpg?v=1775838868","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030015251","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}