{"product_id":"martingale-und-prozesse-paperback","title":"Martingale und Prozesse - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eRené L. Schilling\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis is the third volume of the series \"Moderne Stochastik\" (Modern Stochastics). As a follow-up to the volume \"Wahrscheinlichkeit\" (Probability Theory) it gives an intrdouction to dynamical aspects of probability theory using stochastic processes in discrete time. The first part of the book covers discrete martingales - their convergenc behaviour, optional sampling and stopping, uniform integrability and essential martingale inequalities. The power of martingale techniques is illustrated in the chapters on applications of martingales in classical probability and on the Burkholder-Davis-Gundy inequalities. The second half of the book treats random walks on Zd and Rd, their fluctuation behaviour, recurrence and transience. The last two chapters give a brief introduction to probabilistic potential theory and an outlook of further developments: Brownian motion and Donsker's invariance principle\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eContents\u003cbr\u003e\u003c\/strong\u003eFair Play \u003cbr\u003eConditional Expectation \u003cbr\u003eMartingale \u003cbr\u003eStopping and Localizing \u003cbr\u003eMartingale Convergence \u003cbr\u003e\u003cem\u003eL\u003csup\u003e2\u003c\/sup\u003e\u003c\/em\u003e-Martingales \u003cbr\u003eUniformly Integrable Martingales \u003cbr\u003eSome Classical Results of Probability \u003cbr\u003eElementary Inequalities for Martingales \u003cbr\u003eThe Burkholder-Davis-Gundy Inequalities \u003cbr\u003eRandom Walks on ℤd - the first steps \u003cbr\u003eFluctuations of Simple Random Walks on Z\u003cbr\u003eRecurrence and Transience of General Random Walks\u003cbr\u003eRandom Walks and Analysis\u003cbr\u003eDonsker's Invariance Principle and Brownian Motion \u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eRené L. Schilling\u003c\/strong\u003e, Technische Universität Dresden, Germany. \u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 206\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.4 x 9.4 x 6.6 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e June 01, 2018\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":48620888523001,"sku":"9783110350678","price":35.62,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/W1yMvIe_Uu9783110350678.webp?v=1782978997","url":"https:\/\/bookscloud.io\/products\/martingale-und-prozesse-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}