{"product_id":"9783319509280","title":"Probability Theory and Stochastic Modelling: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics","description":"\u003ch1\u003eProbability Theory and Stochastic Modelling: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics\u003c\/h1\u003e \u003ch2\u003eFayolle, Guy; Iasnogorodski, Roudolf; Malyshev, Vadim\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as \u003ci\u003eStochastic Networks\u003c\/i\u003e, \u003ci\u003eAnalytic Combinatorics\u003c\/i\u003e, and \u003ci\u003eQuantum Physics\u003c\/i\u003e. This second edition consists of two parts.\u003c\/p\u003e\u003cb\u003ePart I\u003c\/b\u003e is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using \u003ci\u003eComplex Function Theory\u003c\/i\u003e, \u003ci\u003eBoundary\u003c\/i\u003e \u003ci\u003eValue Problems\u003c\/i\u003e, \u003ci\u003eRiemann Surfaces\u003c\/i\u003e, and \u003ci\u003eGalois Theory\u003c\/i\u003e, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the \u003ci\u003eTransient Behavior\u003c\/i\u003e of the walks, as well as to find explicit solutions to the one-dimensional \u003ci\u003eQuantum Three-Body Problem\u003c\/i\u003e, or to tackle a new class of \u003ci\u003eIntegrable Systems\u003c\/i\u003e.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003ePart II\u003c\/b\u003e borrows special case-studies from queueing theory (in particular, the famous problem of \u003ci\u003eJoining the Shorter of Two Queues\u003c\/i\u003e) and enumerative combinatorics (\u003ci\u003eCounting\u003c\/i\u003e, \u003ci\u003eAsymptotics\u003c\/i\u003e).\u003c\/p\u003e\u003cp\u003eResearchers and graduate students should find this book very useful.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2017-02-13\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319509280\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-50930-3\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 248\u003c\/p\u003e ","brand":"Springer","offers":[{"title":"Default Title","offer_id":45383438237836,"sku":"9783319509280","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319509280.jpg?v=1775838919","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319509280","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}