Peter W. Glynn

This three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier. If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process.

This book chronicles six decades of exploration and ecological studies of Western American coral reefs, a vibrant and diverse ecosystem in a marginal tropical Pacific region that has long been overlooked. It begins with the discovery of pristine coral reefs in Panama in the 1960s, follows the impact of stressful El Niño warming events that caused widespread coral bleaching and mortality in the 1980s-1990s, documents coral recovery in the late 1990s and early 2000s, and addresses the recent resurgence (2023-24) of extreme El Niño events leading to renewed coral mortality and setbacks in reef recovery. The book delves into the challenges posed by the physical environment, including recurring ENSO activity and increasing ocean acidification, and examines key ecological research topics such as coral reproduction, predation, bioerosion, symbioses, and biodiversity. It also highlights recent molecular genetic advancement in understanding coral endosymbionts, species identification, and phylogenetic relationships. Along the way, personal anecdotes from the eastern Pacific coral research team – ranging from exhilarating to amusing, frightening, and occasionally embarrassing – are shared throughout this scientific journey. This narrative offers a glimpse into the community composition of species and their interactions before severe bleaching and widespread coral mortality, information that is necessary to help guide restoration work. Sketches of coral reef animal associates by Peter W. Glynn and the late Charles Messing add an artistic dimension, highlighting the ecological roles of various species within the reef ecosystem. Many students have made significant contributions to the understanding and conservation of eastern Pacific coral reefs, with several going on to pursue careers in academia, research, and restoration, emerging as the next generation of reef scientists. The book concludes with a cautiously optimistic hope that humanity will shift away from reliance on fossil fuels, and that Generation Z (and their future students) will discover ways to restore coral reefs for future generations.

Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value.

Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value.