LEADER 04588nam 2200661Ia 450 001 9910457240403321 005 20200520144314.0 010 $a1-280-64195-9 010 $a9786610641956 010 $a0-08-046284-7 035 $a(CKB)1000000000357776 035 $a(EBL)270416 035 $a(OCoLC)476003967 035 $a(SSID)ssj0000141985 035 $a(PQKBManifestationID)11161105 035 $a(PQKBTitleCode)TC0000141985 035 $a(PQKBWorkID)10090559 035 $a(PQKB)10093469 035 $a(MiAaPQ)EBC270416 035 $a(PPN)170258025 035 $a(Au-PeEL)EBL270416 035 $a(CaPaEBR)ebr10138585 035 $a(CaONFJC)MIL64195 035 $a(OCoLC)162131411 035 $a(EXLCZ)991000000000357776 100 $a20051213d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDynamic random walks$b[electronic resource] $etheory and applications /$fby Nadine Guillotin-Plantard, Rene? Schott 205 $a1st ed. 210 $aAmsterdam $cElsevier$d2006 215 $a1 online resource (279 p.) 300 $aDescription based upon print version of record. 311 $a0-444-52735-4 320 $aIncludes bibliographical references (p. 249-263) and index. 327 $afront cover; copyright; table of contents; front matter; Preface; body; THEORETICAL ASPECTS; PRELIMINARIES ON DYNAMIC RANDOM WALKS; Introduction; Definitions; A riemannian dynamic random walk; Examples; LIMIT THEOREMS FOR DYNAMIC RANDOM WALKS; A strong law of large numbers; A central limit theorem; A local limit theorem; A Strassen's Functional Law of the Iterated Logarithm; A functional large deviation principle; RECURRENCE AND TRANSIENCE; Introduction; The one-dimensional case; The higher-dimensional case; DYNAMIC RANDOM WALKS IN A RANDOM SCENERY; The recurrent case; The transient case 327 $aA particular dynamical system: The rotation on the torusERGODIC THEOREMS; Introduction; Principal Results; Proof of Theorems 5.4 and 5.5; Proof of Theorem 5.3; Proof of Theorem 5.6; DYNAMIC RANDOM WALKS ON HEISENBERG GROUPS; Introduction; Generalities on Heisenberg groups; Limit theorems; DYNAMIC QUANTUM BERNOULLI RANDOM WALKS; Introduction; Quantum probabilistic notions; Quantum Bernoulli random walks; The dual of SU(2); Quantum Bernoulli random walks as random walks on the dual of SU(2); Dynamic random walks on the dual of SU(2); APPLICATIONS 327 $aDISTRIBUTED ALGORITHMS WITH DYNAMICAL RANDOM TRANSITIONSColliding stacks; The banker algorithm; DATA STRUCTURES WITH DYNAMICAL RANDOM TRANSITIONS; Introduction; Preliminaries; Dynamic linear lists; Dynamic priority queues; Dynamic dictionaries; An example: Linear lists and rotation on the torus; TRANSIENT RANDOM WALKS ON DYNAMICALLY ORIENTED LATTICES; Introduction; Model and results; Proofs; Examples; ASSET PRICING IN DYNAMIC (B,S)-MARKETS; Introduction; Absence of Arbitrage of Dynamic (B,S)-Markets; Completeness of Dynamic (B,S)-Markets 327 $aFair Pricing and Hedging Strategies in Complete Dynamic MarketsGamma-Pricing and Gamma-Hedging; Asymptotic Behavior of Binary (B,S)-markets; back matter; Appendices; A Ergodic theory; Some definitions and basic theorems; Examples of dynamical systems; B Some Results on Diophantine Approximations; C Skorohod metric; D Fourier series; E Hilbert spaces, representations, *-algebras, von Neumann algebras; Hilbert spaces; Lie algebras and representations; *-algebras and von Neumann algebras; References; Index 330 $aThe aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!).· New probabilistic model, new results in probability theory· Original applications in computer science· Applications in mathematical physics· Applications in finance 606 $aRandom walks (Mathematics) 606 $aStochastic processes 608 $aElectronic books. 615 0$aRandom walks (Mathematics) 615 0$aStochastic processes. 676 $a519.282 700 $aGuillotin-Plantard$b Nadine$0627632 701 $aSchott$b Rene?$0352247 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910457240403321 996 $aDynamic random walks$91409288 997 $aUNINA