Focuses on the modification of organisms through genetic manipulation. This work covers topics including molecular biology and ecology, aspects of evolutionary and population genetics, human genetics and genetically modified food. It considers the history of risk assessment and ethical implications with respect to the deliberate release of GMOs.
Focuses on the modification of organisms through genetic manipulation. This work covers topics including molecular biology and ecology, aspects of evo...
The central theme of this book concerns Feynman-Kac path distributions, interacting particle systems, and genealogical tree based models. This re- cent theory has been stimulated from different directions including biology, physics, probability, and statistics, as well as from many branches in engi- neering science, such as signal processing, telecommunications, and network analysis. Over the last decade, this subject has matured in ways that make it more complete and beautiful to learn and to use. The objective of this book is to provide a detailed and self-contained discussion on these...
The central theme of this book concerns Feynman-Kac path distributions, interacting particle systems, and genealogical tree based models. This re- cen...
Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approach this question we introduce and analyze a number of probability models: the Wright-Fisher model, the coalescent, the infinite alleles model, and the infinite sites model. We study the complications that come from nonconstant population size, recombination, population subdivision, and three forms of natural selection: directional selection, balancing selection, and background selection. These theoretical results set the stage for the...
Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approa...
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the...
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, a...
This volume covers recent developments in self-normalized processes, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales.
This volume covers recent developments in self-normalized processes, including self-normalized large and moderate deviations, and laws of the itera...
Three centuries ago Montmort and De Moivre published two books on probability theory emphasizing its most important application at that time, games of chance. This book, on the probabilistic aspects of gambling, is a modern version of those classics.
Three centuries ago Montmort and De Moivre published two books on probability theory emphasizing its most important application at that time, games...
Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation...
Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural science...
The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied...
The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop th...
Since its introduction in 1972, Stein's method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume...
Since its introduction in 1972, Stein's method has offered a completely novel way of evaluating the quality of normal approximations. Through its char...
The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and...
The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from pr...
