{"product_id":"9781468494143","title":"Probability and Its Applications (duplicate)","description":"\u003ch1\u003eProbability and Its Applications (duplicate)\u003c\/h1\u003e \u003ch2\u003eBlumenthal, Robert M.\u003c\/h2\u003e \u003cp\u003eLet {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the \"excursions away from 0,\" that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T \u0026lt; s \u0026lt; t. When one measures the time in t the zero set appropriately (in terms of the local time) the excursions acquire a measure theoretic structure practically identical to that of processes with stationary independent increments, except the values of the process are paths rather than real numbers. And there is a measure on path space that helps describe the measure theoretic properties of the excursions in the same way that the Levy measure describes the jumps of a process with independent increments. The entire circle of ideas is called excursion theory. There are many attractive things about the subject: it is an area where one can use to advantage general probabilistic potential theory to make quite specific calculations, it provides a natural setting for apply­ ing esoteric things like David Williams' path decomposition, it provides a method for constructing processes whose description in terms of an in­ finitesimal generator or some such analytic object would be complicated. And the ideas seem to be closely related to a good deal of current research in probability.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-06-02\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781468494143\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4684-9412-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 276\u003c\/p\u003e ","brand":"Birkhäuser Boston","offers":[{"title":"Default Title","offer_id":44398583218316,"sku":"9781468494143","price":71.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781468494143.jpg?v=1775732641","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781468494143","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}