This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the p...

This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the ...

**NATIONAL BESTSELLER • From the classroom to the courtroom and from financial markets to supermarkets, an intriguing and illuminating look at how randomness, chance, and probability affect our daily lives that will intrigue, awe, and inspire.“Mlodinow writes in a breezy style, interspersing probabilistic mind-benders with portraits of theorists.... The result is a readable crash course in randomness.” —The New York Times Book Review**With the born storyteller's co...

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applic...

This book presents a detailed and contemporary account of the classical theory of convergence of semigroups and its more recent development treating the case where the limit semigroup, in contrast to the approximating semigroups, acts merely on a subspace of the original Banach space (this is the case, for example, with singular perturbations). The author demonstrates the far-reaching applications of this theory using real examples from various branches of pure and applied mathematics, wit...

This book covers the theory of derivatives pricing and hedging as well as techniques used in mathematical finance. The authors use a top-down approach, starting with fundamentals before moving to applications, and present theoretical developments alongside various exercises, providing many examples of practical interest.A large spectrum of concepts and mathematical tools that are usually found in separate monographs are presented here. In addition to the no-arbitrage theory in full...

Scientific progress depends on good research, and good research needs good statistics. But statistical analysis is tricky to get right, even for the best and brightest of us. You'd be surprised how many scientists are doing it wrong.Statistics Done Wrong is a pithy, essential guide to statistical blunders in modern science that will show you how to keep your research blunder-free. You'll examine embarrassing errors and omissions in recent research, learn about the misconce...

The main aim of this bookis to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces.In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are present...

This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicia...

This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic diff...

This lively and engaging book explains the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. The discussion in the book is organized around published studies, as are many of the exercises. Relevant journal articles are reprinted at the back of the book. Freedman makes a thorough appraisal of the statistical methods in these papers and in a variety of other examples. He ill...

In this volume a theory for models of transport in the presence of a free boundary is developed.Macroscopic laws of transport are described by PDE's.When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed.In Part I a free...