Abel-Gontcharoff Pseudopolynomials and Stochastic Applications
Regular price
€138.99
A01=Claude Lefevre
A01=Philippe Picard
Abel-Gontcharoff (A-G) expansions
Abel-Gontcharoff (A-G) pseudopolynomials
applied probability
Author_Claude Lefevre
Author_Philippe Picard
biomathematics
Category=PBT
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
mathematical methodology
randomized parameters
stochastic applications
stochastic models
Taylor formula
Product details
- ISBN 9781836690726
- Publication Date: 24 Oct 2025
- Publisher: ISTE Ltd
- Publication City/Country: GB
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
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.
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.
Philippe Picard is a mathematician and probabilist, and was Professor at the Université de Lyon, France (retired in 2000), where he was responsible for the training of actuaries. His research focuses on mathematical tools in genetics, epidemics and risk theory, such as martingales and polynomials.
Claude Lefèvre is a probabilist and statistician, and is Professor Emeritus at the Université Libre de Bruxelles, Belgium. His research focuses on applied probability models, in particular those related to epidemics, reliability, queueing and actuarial science.
