{"product_id":"stochastic-disorder-problems-9783030015251","title":"Stochastic Disorder Problems","description":"\u003cp\u003e • Author(s): Albert N. Shiryaev\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: System Theory\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\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 The 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.\u003cp\u003e\u003c\/p\u003e Researchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45276869165207,"sku":"9783030015251","price":9460.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783030015251.webp?v=1769286872","url":"https:\/\/atlanticbooks.com\/products\/stochastic-disorder-problems-9783030015251","provider":"Atlantic Books","version":"1.0","type":"link"}