Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.

This volume presents recent developments in the area of Lévy-type processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévy-type process: a non-random function which is a counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levy-type processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.

A perfect blend of medical drama and spiritual insight, Gray Matter is a fascinating account of Dr. David Levy’s decision to begin asking his patients if he could pray for them before surgery. Some are thrilled. Some are skeptical. Some are hostile, and some are quite literally transformed by the request. Each chapter focuses on a specific case, opening with a detailed description of the patient’s diagnosis and the procedure that will need to be performed, followed by the prayer “request.” From there, readers get to look over Dr. Levy’s shoulder as he performs the operation, and then we wait—right alongside Dr. Levy, the patients, and their families—to see the final results. Dr. Levy’s musings on what successful and unsuccessful surgical results imply about God, faith, and the power of prayer are honest and insightful. As we watch him come to his ultimate conclusion that no matter what the results of the procedure are, “God is good,” we cannot help but be truly moved and inspired.

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Packed with images and diagrams, Incredible Elements guides you through the subject one step at a time, from early alchemy to modern-day chemistry. Along the way you'll read about some of the smartest scientists in human history and find out how chemical reactions affect our everyday lives.

A shimmering jewel of a book about writing from two-time Booker Prize finalist Deborah Levy, to publish alongside her new work of nonfiction, The Cost of Living. Blending personal history, gender politics, philosophy, and literary theory into a luminescent treatise on writing, love, and loss, Things I Don't Want to Know is Deborah Levy's witty response to George Orwell's influential essay "Why I Write." Orwell identified four reasons he was driven to hammer at his typewriter--political purpose, historical impulse, sheer egoism, and aesthetic enthusiasm--and Levy's newest work riffs on these same commitments from a female writer's perspective. As she struggles to balance womanhood, motherhood, and her writing career, Levy identifies some of the real-life experiences that have shaped her novels, including her family's emigration from South Africa in the era of apartheid; her teenage years in the UK where she played at being a writer in the company of builders and bus drivers in cheap diners; and her theater-writing days touring Poland in the midst of Eastern Europe's economic crisis, where she observed how a soldier tenderly kissed the women in his life goodbye. Spanning continents (Africa and Europe) and decades (we meet the writer at seven, fifteen, and fifty), Things I Don't Want to Know brings the reader into a writer's heart.

Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.