Abel-Gontcharoff Pseudopolynomials and Stochastic Applications (Hardcover) (ISBN-13: 9781836690726)

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.

Author: Philippe Picard
ISBN-10: 183669072X
ISBN-13: 9781836690726
Publisher: Wiley-Iste
Language: English
Published: 10/24/2025
Pages: 304
Format: Hardcover
Weight: 1.33lbs
Size: 9.21h x 6.14w x 0.69d