Why should we use white noise analysis? Well, one reason of course is that it fills that earlier gap in the tool kit. As Hida would put it, white noise provides us with a useful set of independent coordinates, parametrized by 'time'. And there is a feature which makes white noise analysis extremely user-friendly. Typically the physicist — and not only he — sits there with some heuristic ansatz, like e.g. the famous Feynman 'integral', wondering whether and how this might make sense mathematically. In many cases the characterization theorem of white noise analysis provides the user with a sweet and easy answer. Feynman's 'integral' can now be understood, the 'It's all in the vacuum' ansatz of Haag and Coester is now making sense via Dirichlet forms, and so on in many fields of application. There is mathematical finance, there have been applications in biology, and engineering, many more than we could collect in the present volume.Finally, there is one extra benefit: when we internalize the structures of Gaussian white noise analysis we will be ready to meet another close relative. We will enjoy the important similarities and differences which we encounter in the Poisson case, championed in particular by Y Kondratiev and his group. Let us look forward to a companion volume on the uses of Poisson white noise.The present volume is more than a collection of autonomous contributions. The introductory chapter on white noise analysis was made available to the other authors early on for reference and to facilitate conceptual and notational coherence in their work.

"Why should we use white noise analysis? Well, one reason of course is that it fills that earlier gap in the tool kit. As Hida would put it, white noise provides us with a useful set of independent coordinates, parametrized by "time". And there is a feature which makes white noise analysis extremely user-friendly. Typically the physicist — and not only he — sits there with some heuristic ansatz, like e.g. the famous Feynman "integral", wondering whether and how this might make sense mathematically. In many cases the characterization theorem of white noise analysis provides the user with a sweet and easy answer. Feynman's "integral" can now be understood, the "It's all in the vacuum" ansatz of Haag and Coester is now making sense via Dirichlet forms, and so on in many fields of application. There is mathematical finance, there have been applications in biology, and engineering, many more than we could collect in the present volume. Finally, there is one extra benefit: when we internalize the structures of Gaussian white noise analysis we will be ready to meet another close relative. We will enjoy the important similarities and differences which we encounter in the Poisson case, championed in particular by Y Kondratiev and his group. Let us look forward to a companion volume on the uses of Poisson white noise. The present volume is more than a collection of autonomous contributions. The introductory chapter on white noise analysis was made available to the other authors early on for reference and to facilitate conceptual and notational coherence in their work."--Publisher's website.

NATIONAL BOOK AWARD WINNER • An “eerie, brilliant, and touching” (The New York Times) modern classic about mass culture and the numbing effects of technology. “Tremendously funny . . . A stunning performance from one of our most intelligent novelists.”—The New Republic The inspiration for the award-winning major motion picture starring Adam Driver and Greta Gerwig Jack Gladney teaches Hitler Studies at a liberal arts college in Middle America where his colleagues include New York expatriates who want to immerse themselves in “American magic and dread.” Jack and his fourth wife, Babette, bound by their love, fear of death, and four ultramodern offspring, navigate the usual rocky passages of family life to the background babble of brand-name consumerism. Then a lethal black chemical cloud floats over their lives, an “airborne toxic event” unleashed by an industrial accident. The menacing cloud is a more urgent and visible version of the “white noise” engulfing the Gladney family—radio transmissions, sirens, microwaves, ultrasonic appliances, and TV murmurings—pulsing with life, yet suggesting something ominous.

The National Book Award-winning classic from the author of Underworld and Libra, now a major motion picture starring Adam Driver and Greta Gerwig White Noise tells the story of Jack Gladney, his fourth wife, Babette, and four ultra­modern offspring as they navigate the rocky passages of family life to the background babble of brand-name consumerism. When an industrial accident unleashes an "airborne toxic event," a lethal black chemical cloud floats over their lives. The menacing cloud is a more urgent and visible version of the "white noise" engulfing the Gladneys—radio transmissions, sirens, microwaves, ultrasonic appliances, and TV murmurings—pulsing with life, yet suggesting something ominous. For more than sixty-five years, Penguin has been the leading publisher of classic literature in the English-speaking world. With more than 1,500 titles, Penguin Classics represents a global bookshelf of the best works throughout history and across genres and disciplines. Readers trust the series to provide authoritative texts enhanced by introductions and notes by distinguished scholars and contemporary authors, as well as up-to-date translations by award-winning translators.

Understanding Jonathan Lethem is a study of the novels, short fiction, and nonfiction on a wide range of subjects in the arts by American novelist Jonathan Lethem, who is the recipient of the National Book Critics Circle Award for Fiction for Motherless Brooklyn, a MacArthur Foundation "genius" grant, and the Locus Award for Best First Novel for Gun, with Occasional Music. Matthew Luter explores the key contemporaries of and influences on Lethem, who is the Roy Edward Disney Professor of Creative Writing at Pomona College. Luter begins this volume by explaining how Lethem's innovative and provocative essay on creative appropriation, "The Ecstasy of Influence," differs from other writing about influence, suggesting an artistic mode that celebrates thoughtful borrowing. Readings of Lethem's three major novels follow: taken together, Motherless Brooklyn, The Fortress of Solitude, and Chronic City present a novelist coming to terms with the joys and downsides of artistic influence. Luter concludes the edition with an examination of Lethem's third collection, Lucky Alan: And Other Stories. Borrowing openly and promiscuously from earlier traditions both high and low (experimental fiction, comic books, art film, detective novels), Lethem displays a career-long interest in questioning what literary originality might mean in a postmodern age. Some suggest that such borrowings indicate a literary well that has run dry, making writers such as Lethem mere patchwork artists. Luter argues instead that Lethem's propensity for wearing his influences and obsessions on his sleeve encourages new thought about originality itself. Out with "it's all been done" and in with "look at all that's been done, and all that we can still do with it!"

Perfect for expecting parents who want to provide a soothing home for the newest member of their family, The Happiest Baby on the Block, the national bestseller by respected pediatrician and child development expert Dr. Harvey Karp, is a revolutionary method for calming a crying infant and promoting healthy sleep from day one. In perhaps the most important parenting book of the decade, Dr. Harvey Karp reveals an extraordinary treasure sought by parents for centuries --an automatic “off-switch” for their baby’s crying. No wonder pediatricians across the country are praising him and thousands of Los Angeles parents, from working moms to superstars like Madonna and Pierce Brosnan, have turned to him to learn the secrets for making babies happy. Never again will parents have to stand by helpless and frazzled while their poor baby cries and cries. Dr. Karp has found there IS a remedy for colic. “I share with parents techniques known only to the most gifted baby soothers throughout history …and I explain exactly how they work.” In a innovative and thought-provoking reevaluation of early infancy, Dr. Karp blends modern science and ancient wisdom to prove that newborns are not fully ready for the world when they are born. Through his research and experience, he has developed four basic principles that are crucial for understanding babies as well as improving their sleep and soothing their senses: ·The Missing Fourth Trimester: as odd as it may sound, one of the main reasons babies cry is because they are born three months too soon. ·The Calming Reflex: the automatic reset switch to stop crying of any baby in the first few months of life. ·The 5 “S’s”: the simple steps (swaddling, side/stomach position, shushing, swinging and sucking) that trigger the calming reflex. For centuries, parents have tried these methods only to fail because, as with a knee reflex, the calming reflex only works when it is triggered in precisely the right way. Unlike other books that merely list these techniques Dr. Karp teaches parents exactly how to do them, to guide cranky infants to calm and easy babies to serenity in minutes…and help them sleep longer too. ·The Cuddle Cure: the perfect mix the 5 “S’s” that can soothe even the most colicky of infants. In the book, Dr. Karp also explains: What is colic? Why do most babies get much more upset in the evening? How can a parent calm a baby--in mere minutes? Can babies be spoiled? When should a parent of a crying baby call the doctor? How can a parent get their baby to sleep a few hours longer? Even the most loving moms and dads sometimes feel pushed to the breaking point by their infant’s persistent cries. Coming to the rescue, however, Dr. Karp places in the hands of parents, grandparents, and all childcare givers the tools they need to be able to calm their babies almost as easily as…turning off a light. From the Hardcover edition.

This book gives a systematic, comprehensive, and unified account of modern nonparametric statistics of density estimation, nonparametric regression, filtering signals, and time series analysis. The companion software package, available over the Internet, brings all of the discussed topics into the realm of interactive research. Virtually every claim and development mentioned in the book is illustrated with graphs which are available for the reader to reproduce and modify, making the material fully transparent and allowing for complete interactivity.

This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.

From the Pulitzer Prize-winning playwright of Topdog/Underdog comes a play about race and friendship in a deeply flawed society.

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.