UID:
almahu_9947367622502882
Format:
1 online resource (279 p.)
Edition:
1st ed.
ISBN:
1-280-64195-9
,
9786610641956
,
0-08-046284-7
Content:
The 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
Note:
Description based upon print version of record.
,
front 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
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A 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
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DISTRIBUTED 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
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Fair 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
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English
Additional Edition:
ISBN 0-444-52735-4
Language:
English
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