02884nam 22005775 450 99646667150331620200705014402.03-319-25372-710.1007/978-3-319-25372-5(CKB)4340000000001636(SSID)ssj0001657186(PQKBManifestationID)16438129(PQKBTitleCode)TC0001657186(PQKBWorkID)14989493(PQKB)10924566(DE-He213)978-3-319-25372-5(MiAaPQ)EBC6298278(MiAaPQ)EBC5586682(Au-PeEL)EBL5586682(OCoLC)1066184452(PPN)191292362(EXLCZ)99434000000000163620160204d2015 u| 0engurnn#008mamaatxtccrBranching Random Walks[electronic resource] École d'Été de Probabilités de Saint-Flour XLII – 2012 /by Zhan Shi1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (X, 133 p. 8 illus., 6 illus. in color.)École d'Été de Probabilités de Saint-Flour,0721-5363 ;2151Bibliographic Level Mode of Issuance: Monograph3-319-25371-9 I Introduction -- II Galton–Watson trees -- III Branching random walks and martingales -- IV The spinal decomposition theorem -- V Applications of the spinal decomposition theorem -- VI Branching random walks with selection -- VII Biased random walks on Galton–Watson trees -- A Sums of i.i.d. random variables -- References.Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time. Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.     .École d'Été de Probabilités de Saint-Flour,0721-5363 ;2151ProbabilitiesProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Probabilities.Probability Theory and Stochastic Processes.519.282Shi Zhanauthttp://id.loc.gov/vocabulary/relators/aut718982MiAaPQMiAaPQMiAaPQBOOK996466671503316Branching random walks1395535UNISA