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Le but de cet ouvrage est de presenter un panorama de differentes methodes mathematiques utilisees pour la modelisation de phenomenes issus du vivant. Nous avons voulu etre le plus large possible, incluant ainsi a la fois les methodes deterministes (systemes dynamiques, theorie des jeux) et les methodes stochastiques (processus aleatoires, statistiques). Chaque modele mathematique propose est accompagne d'un exemple concret eclairant la modelisation retenue.

This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stephane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian...