Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.

A limit order book is essentially a file on a computer that contains all orders sent to the market, along with their characteristics such as the sign of the order, price, quantity and a timestamp. The majority of organized electronic markets rely on limit order books to store the list of interests of market participants on their central computer. A limit order book contains all the information available on a specific market and it reflects the way the market moves under the influence of its participants. This book discusses several models of limit order books. It begins by discussing the data to assess their empirical properties, and then moves on to mathematical models in order to reproduce the observed properties. Finally, the book presents a framework for numerical simulations. It also covers important modelling techniques including agent-based modelling, and advanced modelling of limit order books based on Hawkes processes. The book also provides in-depth coverage of simulation techniques and introduces general, flexible, open source library concepts useful to readers studying trading strategies in order-driven markets.

Three-part treatment introduces basics plus theory of stochastic differential equations and various limit theorems connected with convergence of sequence of Markov chains to Markov process with continuous time. 1965 edition.

The Avian Empire is locked in an endless war that has claimed the lives of countless Fledge men and women. Their mindless enemy is inexhaustible. There is no option for peace, the monsters can’t be reasoned with and they will never stop. Most in Avian society never get a chance to mature and grow their white feathered wings and take to the skies. Most never get to master communication with their Scala, the semi sentient scales that cover their body. Fledges are raised to serve a purpose of preservation or die in the depths. Ellie, a young Avian Fledge living on the Plymouth Plateau, startles awake from a reoccurring dream—one where she suddenly grows wings and takes to the skies. As an Avian Fledge, Ellie struggles to thrive in her harsh society—one where women are treated like cattle and where the Fledges constantly fear their mysterious rulers, the Mature Avians. Destined to repeat the life of her Mother and countless other fledge women. Ellie will embark on a journey in which she will gain tremendous power and suffer incredible loss. She will battle the balance of what it means to be a monster or a savior. With this unexpected power, she will soar to new heights and change the world. Whether that change is for good or evil, will depend on her belief that the world she has known is worth saving or should be changed forever.

The legendary author of The Outsiders returns with her first new novel in more than fifteen years! An orphan and a bastard, Jamie grew up tough enough to handle almost anything. He survived foreign prisons, smugglers, pirates, gunrunners, and shark attacks. But what he finds in the quote town of Hawkes Harbor, Delaware, was enough to drive him almost insane—and change his life forever. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

The blistering story of a young man making his Broadway debut in Henry IV just as his marriage implodes—a "witty, wise, and heartfelt novel" (Washington Post) about art and love, fame and heartbreak from the acclaimed actor/writer/director. A bracing meditation on fame and celebrity, and the redemptive, healing power of art; a portrait of the ravages of disappointment and divorce; a poignant consideration of the rites of fatherhood and manhood; a novel soaked in rage and sex, longing and despair; and a passionate love letter to the world of theater, A Bright Ray of Darkness showcases Ethan Hawke's gifts as a novelist as never before. Hawke's narrator is a young man in torment, disgusted with himself after the collapse of his marriage, still half hoping for a reconciliation that would allow him to forgive himself and move on as he clumsily, and sometimes hilariously, tries to manage the wreckage of his personal life with whiskey and sex. What saves him is theater: in particular, the challenge of performing the role of Hotspur in a production of Henry IV under the leadership of a brilliant director, helmed by one of the most electrifying—and narcissistic—Falstaff's of all time. Searing, raw, and utterly transfixing, A Bright Ray of Darkness is a novel about shame and beauty and faith, and the moral power of art.

From the Introduction: " The emphasis has been placed on topics of interest in systems science at large...The level of exposition and the inclusion of a large number of exercises with complete detailed solutions make this book usable as a text for graduate students in applied probability, electrical engineering, computer science, and operations research. The prerequisites in probability and random processes are recalled in the Appendices."

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.

We consider the nonlinear filtering problem for partially observed Generalized Hawkes Processes, which can be applied in the context of portfolio credit risk. The problem belongs to the larger class of hidden Markov models, where the counting process is observed at discrete points in time and the observations are sparse, while the intensity driving process in unobservable. We construct the conditional distribution of the process given the information filtration and we discuss the analytical and numerical properties of the corresponding filters. In particular, we study the sensitivity of the filters with respect to the parameters of the model, and we obtain a monotonicity result with respect to the jump and the volatility terms driving the intensity. Using the scaled process, we provide necessary and sufficient conditions for the frequency of time observations in terms of the parameters of the model, to ensure a good performance of the filter. We also address the problem of parameter estimation for the Generalized Hawkes Process in the framework of the EM algorithm, and we analyze the effect of the self-exciting feature of our process on the asymptotic and numerical properties of the estimators.

This book covers the mathematical idea of branching processes, and tailors it for a biological audience.