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Abel-Gontcharoff Pseudopolynomials and Stochastic Applications出版済み 3-5週間でお届けいたします。
Title: Abel-Gontcharoff Pseudopolynomials and Stochastic Applications Series: ISTE Invoiced Author: Picard, Philippe (Universite de Lyon, France) / Lefevre, Claude (Universite Libre de Bruxelles, Belgium) Publisher: WILEY ISBN: 9781836690726 Cover: HARDCOVER Date: 2025年10月 こちらの商品は学校・法人様向け（機関契約）のオンラインブック版がございます。 オンラインブックの価格、納期につきましては弊社営業員または当ECサイトよりお問い合わせください。  DESCRIPTION This book proposes a new mathematical methodology for addressing first passage problems, particularly in various classical stochastic models of applied probability. This approach is based on the so-called Abel-Gontcharoff (A-G) pseudopolynomials and the associated A-G expansions, which have been introduced and studied by the authors in recent years. These A-G expansions generalize the well-known Abel expansion, which allows us to extend the standard Taylor formula. Abel-Gontcharoff Pseudopolynomials and Stochastic Applications starts by presenting an in-depth presentation of the general theory, and then moves onto stochastic applications of this theory, especially in biomathematics. Univariate and multivariate versions of the A-G pseudopolynomials, as well as extensions with randomized parameters, are discussed and illustrated for modeling, notably by highlighting families of martingales and using stopping time theorems. This book concludes by paving the way to a nonhomogeneous theory for first crossing problems. TABLE OF CONTENTS Chapter 1. Historical Abel-Gontcharoff Polynomials 1.1. Abel identity 1.2. Abel polynomials and expansions 1.3. Gontcharoff contribution 1.4. Increased recognition 1.5. A first meeting problem 1.6. A final epidemic outcome 1.7. A goodness-of-fit test 1.8. Extension to pseudopolynomials Chapter 2. Abel-Gontcharoff Pseudopolynomials 2.1. General framework: D, E, F,Δ 2.2. Copies Ε and standard families 2.3. An integration operator Iu 2.4. A-G pseudopolynomials Gn( |U) 2.5. Expansions of A-G type 2.6. A shift operator Sa 2.7. A multiplication operator Mλ 2.8. Shift invariance property Chapter 3. General Theory and Explicit Results 3.1. Return to the shift invariance 3.2. The higher dimensional case 3.3. Calculation formulas for ¯Gn( |U) 3.4. Geometric or affine form for U 3.5. Extension to special sequences ui = {ui,j} 3.6. When D is the set of integers Chapter 4. Further Results and Properties 4.1. A related basic family E(b) 4.2. Upper and lower bounds for Gn( |U) 4.3. Short visit to the A-G type series 4.4. Bilinear forms and biorthogonality 4.5. An alternative generalization Chapter 5. Multi-index A-G Pseudopolynomials 5.1. Key definitions and expansions 5.2. Explicit formulas for Gn1,n2( |U) 5.3. Multivariate case Gn1,n2( |U(1), U(2)) 5.4. Integral multivariate representation 5.5. Special case of A-G polynomials Chapter 6. Randomizing A-G Pseudopolynomials 6.1. How to integrate stochasticity? 6.2. With ui partial sums of i.i.d. variables 6.3. Multivariate additive extension 6.4. With ui partial products of i.i.d. variables 6.5. Multivariate multiplicative extension 6.6. Additive case for exponential functions Chapter 7. First Meeting Level with a Lower Boundary 7.1. Return to a classical Poisson process 7.2. For a compound Poisson process 7.3. Related first passage problems 7.4. With the number of Poisson jumps 7.5. For a linear birth process with immigration 7.6. Extension allowing multiple births 7.7. For a nonlinear birth process Chapter 8. Less Standard First Meeting Models 8.1. Compound Poisson process with a renewal process 8.2. Linear birth process with a renewal process 8.3. Nonlinear death process with a birth process 8.4. Binomial process with a lower boundary 8.5. For a compound binomial process 8.6. Compound binomial process with a renewal process Chapter 9. Martingales and A-G Pseudopolynomials 9.1. Motivation via damage-type models 9.2. Unified treatment by A-G pseudopolynomials 9.3. Reed-Frost multipopulation epidemic 9.4. Nonlinear death process 9.5. Combined general and fatal epidemics 9.6. Time-dependent bivariate death proces Chapter 10. Towards a Non-homogeneous Theory 10.1. A non-stationary compound Poisson process 10.2. A compound Poisson random field 最近チェックした商品
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