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  • 1
    Online Resource
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    Dynamic random walks : theory and applications (2006)
    Amsterdam ; Boston ; Oxford : Elsevier
    Details
    UID:
    b3kat_BV036962290
    Format: 1 Online-Ressource (xii, 266 p.) , ill , 25 cm
    Edition: 1st ed
    Edition: Online-Ausgabe Elsevier e-book collection on ScienceDirect Sonstige Standardnummer des Gesamttitels: 041169-3
    ISBN: 0444527354 , 9780444527356
    Note: Includes bibliographical references (p. 249-263) and index
    Additional Edition: Reproduktion von Dynamic random walks 2006
    Language: English
    Subjects: Mathematics
    RVK:
    SK 820
    Keywords: Electronic books ; Electronic books
    URL: Volltext
    URL: Volltext
    URL: Volltext  (Deutschlandweit zugänglich)
    URL: https://doi.org/10.1016/B978-0-444-52735-6.X5037-4
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  • 2
    Online Resource
    Online Resource
    Probabilistic and Statistical Methods in Computer Science (2001)
    Boston, MA :Springer US :
    Details
    UID:
    almahu_9947363071902882
    Format: XVI, 236 p. 11 illus. , online resource.
    ISBN: 9781475762808
    Content: Probabilistic and Statistical Methods in Computer Science presents a large variety of applications of probability theory and statistics in computer science and more precisely in algorithm analysis, speech recognition and robotics. It is written on a self-contained basis: all probabilistic and statistical tools needed are introduced on a comprehensible level. In addition all examples are worked out completely. Most of the material is scattered throughout available literature. However, this is the first volume that brings together all of this material in such an accessible format. Probabilistic and Statistical Methods in Computer Science is intended for students in computer science and applied mathematics, for engineers and for all researchers interested in applications of probability theory and statistics. It is suitable for self study as well as being appropriate for a course or seminar.
    Note: I Preliminaries -- 1. Probabilistic Tools -- 2. Statistical Tools -- II Applications -- 3. Some Applications in Algorithmics -- 4. Some Applications in Speech Recognition -- 5. Some Applications in Robotics -- Appendices -- A— Some useful statistical programs -- 1. The Gaussian density class -- 2. The Centroid class -- 3. The Top down clustering program -- References.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9781441948779
    Language: English
    DOI: 10.1007/978-1-4757-6280-8
    URL: http://dx.doi.org/10.1007/978-1-4757-6280-8
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  • 3
    Online Resource
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    Dynamic random walks : theory and applications (2006)
    Amsterdam :Elsevier,
    Details
    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 , 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 , 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 , 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 , English
    Additional Edition: ISBN 0-444-52735-4
    Language: English
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    HU Berlin
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  • 4
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    Book
    Stochastic processes and operator calculus on quantum groups (1999)
    Dordrecht [u.a.] : Kluwer Academic Publishers
    Details
    UID:
    b3kat_BV013684976
    Format: VII, 227 S.
    ISBN: 079235883X
    Series Statement: Mathematics and its applications 490
    Language: English
    Subjects: Mathematics
    RVK:
    SK 820
    Keywords: Stochastischer Prozess ; Operatorenrechnung ; Quantengruppe
    URL: Inhaltsverzeichnis
    URL: Inhaltsverzeichnis
    URL: Cover
    URL: Inhaltstext
    URL: http://www.loc.gov/catdir/enhancements/fy0822/99038083-t.html
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  • 5
    Book
    Book
    Random generation of trees : random generators in computer science (1995)
    Boston [u.a.] :Kluwer Acad. Publ.,
    Details
    UID:
    almahu_BV010259303
    Format: XI, 208 S. : Ill., graph. Darst.
    ISBN: 0-7923-9528-X
    Language: English
    Subjects: Computer Science , Mathematics
    RVK:
    SK 890
    RVK:
    ST 130
    Keywords: Zufallsvariable ; Baum ; Algorithmus
    URL: http://www.loc.gov/catdir/enhancements/fy0820/94039286-d.html
    URL: http://www.loc.gov/catdir/enhancements/fy0820/94039286-t.html
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  • 6
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    Algebraic Structures and Operator Calculus : Volume II: Special Functions and Computer Science (1994)
    Dordrecht :Springer Netherlands,
    Details
    UID:
    almahu_9947362882702882
    Format: X, 150 p. , online resource.
    ISBN: 9780585280035
    Series Statement: Mathematics and Its Applications ; 292
    Content: In this volume we will present some applications of special functions in computer science. This largely consists of adaptations of articles that have appeared in the literature . Here they are presented in a format made accessible for the non-expert by providing some context. The material on group representations and Young tableaux is introductory in nature. However, the algebraic approach of Chapter 2 is original to the authors and has not appeared previously . Similarly, the material and approach based on Appell states, so formulated, is presented here for the first time . As in all volumes of this series, this one is suitable for self-study by researchers . It is as well appropriate as a text for a course or advanced seminar . The solutions are tackled with the help of various analytical techniques, such as g- erating functions, and probabilistic methods/insights appear regularly . An interesting feature is that, as has been the case in classical applications to physics, special functions arise- here in complexity analysis. And, as in physics, their appearance indicates an underlying Lie structure. Our primary audience is applied mathematicians and theoretical computer scientists . We are quite sure that pure mathematicians will find this volume interesting and useful as well .
    Note: Basic Data Structures -- Data Structures & Orthogonal Polynomials -- Applications of Bessel Functions and Lommel Polynomials -- Fourier Transform on Finite Groups and Related Transforms -- Young Tableaux and Combinatorial Enumeration in Parallel Processing.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780792329213
    Language: English
    DOI: 10.1007/978-0-585-28003-5
    URL: http://dx.doi.org/10.1007/978-0-585-28003-5
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  • 7
    Online Resource
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    Stochastic Processes and Operator Calculus on Quantum Groups (1999)
    Dordrecht :Springer Netherlands :
    Details
    UID:
    almahu_9947363251102882
    Format: VIII, 232 p. , online resource.
    ISBN: 9789401592772
    Series Statement: Mathematics and Its Applications ; 490
    Note: 1 Introduction -- 2 Preliminaries on Lie groups -- 3 Hopf algebras, quantum groups and braided spaces -- 4 Stochastic processes on quantum groups -- 5 Markov structure of quantum Lévy processes -- 6 Diffusions on braided spaces -- 7 Evolution equations and Lévy processes on quantum groups -- 8 Gauss laws in the sense of Bernstein on quantum groups -- 9 Phase retrieval for probability distributions on quantum groups and braided groups -- 10 Limit theorems on quantum groups.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9789048152902
    Language: English
    DOI: 10.1007/978-94-015-9277-2
    URL: http://dx.doi.org/10.1007/978-94-015-9277-2
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  • 8
    Online Resource
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    Algebraic Structures and Operator Calculus : Volume III: Representations of Lie Groups (1996)
    Dordrecht :Springer Netherlands,
    Details
    UID:
    almahu_9947363394402882
    Format: IX, 230 p. , online resource.
    ISBN: 9789400901575
    Series Statement: Mathematics and Its Applications ; 347
    Content: Introduction I. General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 II. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 III. Lie algebras: some basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 II. Holomorphic canonical calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 III. Canonical Appell systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Chapter 2 Representations of Lie groups I. Coordinates on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 II. Dual representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 III. Matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 IV. Induced representations and homogeneous spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 General Appell systems Chapter 3 I. Convolution and stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 II. Stochastic processes on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 III. Appell systems on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Chapter 4 Canonical systems in several variables I. Homogeneous spaces and Cartan decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 II. Induced representation and coherent states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 III. Orthogonal polynomials in several variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Chapter 5 Algebras with discrete spectrum I. Calculus on groups: review of the theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 II. Finite-difference algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 III. q-HW algebra and basic hypergeometric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 IV. su2 and Krawtchouk polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 V. e2 and Lommel polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Chapter 6 Nilpotent and solvable algebras I. Heisenberg algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 II. Type-H Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Vll III. Upper-triangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 IV. Affine and Euclidean algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Chapter 7 Hermitian symmetric spaces I. Basic structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 II. Space of rectangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 III. Space of skew-symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 IV. Space of symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Chapter 8 Properties of matrix elements I. Addition formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 II. Recurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 III. Quotient representations and summation formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Chapter 9 Symbolic computations I. Computing the pi-matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 II. Adjoint group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 III. Recursive computation of matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
    Note: I. General remarks -- II. Notations -- III. Lie algebras: some basics -- 1 Operator calculus and Appell systems -- I. Boson calculus -- II. Holomorphic canonical calculus -- III. Canonical Appell systems -- 2 Representations of Lie groups -- I. Coordinates on Lie groups -- II. Dual representations -- III. Matrix elements -- IV. Induced representations and homogeneous spaces -- 3 General Appell systems -- I. Convolution and stochastic processes -- II. Stochastic processes on Lie groups -- III. Appell systems on Lie groups -- 4 Canonical systems in several variables -- I. Homogeneous spaces and Cartan decompositions -- II. Induced representation and coherent states -- III. Orthogonal polynomials in several variables -- 5 Algebras with discrete spectrum -- I. Calculus on groups: review of the theory -- II. Finite-difference algebra -- III. q-HW algebra and basic hypergeometric functions -- IV. su2 and Krawtchouk polynomials -- V. e2 and Lommel polynomials -- 6 Nilpotent and solvable algebras -- I. Heisenberg algebras -- II. Type-H Lie algebras -- III. Upper-triangular matrices -- IV. Affine and Euclidean algebras -- 7 Hermitian symmetric spaces -- I. Basic structures -- II. Space of rectangular matrices -- III. Space of skew-symmetric matrices -- IV. Space of symmetric matrices -- 8 Properties of matrix elements -- I. Addition formulas -- II. Recurrences -- III. Quotient representations and summation formulas -- 9 Symbolic computations -- I. Computing the pi-matrices -- II. Adjoint group -- III. Recursive computation of matrix elements -- IV. Symbolic computation of Appell systems -- MAPLE output and procedures -- References.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9789401065573
    Language: English
    DOI: 10.1007/978-94-009-0157-5
    URL: http://dx.doi.org/10.1007/978-94-009-0157-5
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  • 9
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    Algebraic Structures and Operator Calculus : Volume I: Representations and Probability Theory (1993)
    Dordrecht : Springer Netherlands
    Details
    UID:
    b3kat_BV042423853
    Format: 1 Online-Ressource (IX, 226 p)
    ISBN: 9789401116480 , 9789401047203
    Series Statement: Mathematics and Its Applications 241
    Note: This series presents some tools of applied mathematics in the areas of probability theory, operator calculus, representation theory, and special functions used currently, and we expect more and more in the future, for solving problems in mathematics, physics, and, now, computer science. Much of the material is scattered throughout available literature, however, we have nowhere found in accessible form all of this material collected. The presentation of the material is original with the authors. The presentation of probability theory in connection with group representations is new, this appears in Volume I. Then the applications to computer science in Volume II are original as well. The approach found in Volume III, which deals in large part with infinite-dimensional representations of Lie algebras/Lie groups, is new as well, being inspired by the desire to find a recursive method for calculating group representations. One idea behind this is the possibility of symbolic computation of the matrix elements. In this volume, Representations and Probability Theory, we present an introduction to Lie algebras and Lie groups emphasizing the connections with operator calculus, which we interpret through representations, principally, the action of the Lie algebras on spaces of polynomials. The main features are the connection with probability theory via moment systems and the connection with the classical elementary distributions via representation theory. The various systems of polynomials that arise are one of the most interesting aspects of this study
    Language: English
    DOI: 10.1007/978-94-011-1648-0
    URL: Volltext
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  • 10
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    Book
    Algebraic structures and operator calculus; Vol. 2: Special functions and computer science (1994)
    Dordrecht [u.a.] : Kluwer
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    UID:
    gbv_156531186
    Format: IX, 148 S , 25 cm
    ISBN: 079232921x
    Series Statement: Mathematics and its applications 292
    Note: Literaturverz. S. 139 - 143
    In: Vol. 2
    Language: English
    Keywords: Heaviside-Kalkül
    URL: Inhaltstext
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