Bøger i Lecture Notes in Mathematics serien

The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems.

This volume presents recent developments in the area of Levy-type processes and more general stochastic processes that behave locally like a Levy process.

In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits.

The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Levy processes. The chapters cover the main aspects of the estimation of discretely observed Levy processes, when the observation scheme is regular, from an up-to-date viewpoint.

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory.

This book presents the state of the art in mathematical research on modelling the mechanics of biological systems - a science at the intersection between biology, mechanics and mathematics known as mechanobiology.

The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincare inequalities, and spectral synthesis theorems.

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained.