Harold Kushner

With the same compassion and wisdom that powered his phenomenal bestseller When Bad Things Happen to Good People, Harold Kushner addresses a need that is universal and timeless -- the wish for a meaningful life. Why is it that, after attaining many of our goals, we are left with a sense that something vital is missing? In his deeply inspiring bestseller, Rabbi Kushner shows us how to live as human beings are meant to. He guides us to a heightened sense of joy, purpose, and meaning, and helps us to redirect our energies toward goals that will bring us lasting happiness and true fulfillment.

The Search for a Life That Matters

When All You've Ever Wanted Isn't Enough

From the author of When Bad Things Happen to Good People comes an inspiring new bestseller that puts human feelings of guilt and inadequacy in perspective - and teaches us how we can learn to accept ourselves and others even when we and they are less than perfect. How Good Do We Have to Be? is for everyone who experiences that sense of guilt and disappointment. Harold Kushner, writing with his customary generosity and wisdom, shows us how human life is too complex for anyone to live it without making mistakes, and why we need not fear the loss of God's love when we are less than perfect. Harold Kushner begins by offering a radically new interpretation of the story of Adam and Eve, which he sees as a tale of Paradise Outgrown rather than Paradise Lost: eating from the Tree of Knowledge was not an act of disobedience, but a brave step forward toward becoming human, complete with the richness of work, sexuality and child-rearing, and a sense of our mortality. Drawing on modern literature, psychology, theology,,and his own thirty years of experience as a congregational rabbi, Harold Kushner reveals how acceptance and forgiveness can change our relationships with the most important people in our lives and help us meet the bold and rewarding challenge of being human.

A New Understanding of Guilt and Forgiveness

How Good Do We Have to Be?

The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems

Paul G. Dupuis

This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new prob lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for mulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. Both the "drift" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.

Numerical Methods for Stochastic Control Problems in Continuous Time

G. George Yin

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.

Stochastic Approximation and Recursive Algorithms and Applications

Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.

The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. The book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is either in the use of the algorithms or in the mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.

Harold Kushner

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