Samuel Karlin

Michael Stevens has always been a long shot. After a decade of tennis and travel, he's arrived at the end of the road. With his ranking in ruins and his bank account running on empty, Michael has come to Tokyo with one last chance to mend a broken heart and prove who he is both on the court and off. Can he win against all odds? Will he discover that winning doesn't have anything to do with tennis at all? In this coming of age story of love, loss and second chances, Michael has one more shot to show what he can do and finally figure out what really matters in life.

Stochastic Processes: Holden-Day Series In Probability And Statistics is a comprehensive textbook written by Emanuel Parzen. The book provides an in-depth study of stochastic processes, which are mathematical models used to describe random phenomena that evolve over time. The book covers a wide range of topics, including Markov processes, Poisson processes, Brownian motion, and martingales. It also includes discussions on the applications of stochastic processes in various fields, such as finance, engineering, and physics. The book is divided into four parts, each focusing on different aspects of stochastic processes. Part I introduces the basic concepts of stochastic processes, such as probability spaces, random variables, and conditional expectations. Part II covers discrete-time Markov processes, including their properties, classification, and applications. Part III discusses continuous-time Markov processes, including Poisson processes, birth-death processes, and diffusion processes. Part IV covers martingales, which are stochastic processes that have a property of being fair games. The book is written in a clear and concise manner, with numerous examples and exercises to help readers understand the concepts. It is suitable for graduate students and researchers in mathematics, statistics, and related fields who want to deepen their understanding of stochastic processes. Overall, Stochastic Processes: Holden-Day Series In Probability And Statistics is an essential reference for anyone interested in the theory and applications of stochastic processes. This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition: Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications Plentiful, completely updated problems Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers New chapters of stochastic differential equations and Brownian motion and related processes Additional sections on Martingale and Poisson process

This book deals with a key area of population genetics: the ratio of the sexes in a population, or the allocation of resources to male versus female reproductive function. Samuel Karlin and Sabin Lessard establish the formal theoretical aspects of the evolution of sex ratio within the constraints of genetic mechanisms of sex determination. Their results generalize and unify existing work on the topic, strengthening previous conceptions in some cases and, in other instances, offering new directions of research. There are two main approaches to understanding the causes and effects of sex ratio. One approach focuses on the optimization and adaptive functions of sex allocation, while the other emphasizes the consequences of genetic sex determination mechanisms. In discussing the utility of these two approaches, Professors Karlin and Lessard examine the principal sex-determining mechanisms and facts involved in sex ratio representations, the various genetic and environmental factors that contribute to adaptive sex expression, and the evolution of sex determining systems and controls. From a population genetic perspective, the authors derive evolutionary properties in support of the high incidence of 1:1 sex ratio in natural populations and investigate the conditions that can explain the occurrence of biased sex ratio.

This Second Course continues the development of the theory and applications of stochastic processes as promised in the preface of A First Course. We emphasize a careful treatment of basic structures in stochastic processes in symbiosis with the analysis of natural classes of stochastic processes arising from the biological, physical, and social sciences.

The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other. The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.