R.J. Williams - Böcker

A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability.Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then It’s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman–Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed.New to the second edition are a discussion of the Cameron–Martin–Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use.This book willbe a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis.The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. —Journal of the American Statistical Association An attractive text…written in [a] lean and precise style…eminently readable. Especially pleasant are the care and attention devoted to details… A very fine book.—Mathematical Reviews

In the heart of Victorian London, fearless journalist and suffragist, Verity Mallard, finds herself entangled in a web of mystery and danger. When her barrister brother, Mortimer, aids Mrs Clara Powell in a divorce case, he discovers that her husband is the bearer of a sinister secret. As they delve into the seedy underbelly of the East End, the siblings, aided by the tenacious private investigator, George Benson, uncover a chilling truth-their target is a depraved murderer. However, a twist of fate destroys the evidence they desperately need to bring him to book. Realising that justice may slip through the cracks, Verity persuades George and Mortimer to embark on a perilous plan to neutralise the killer.

In 1895 London, spirited journalist Verity Mallard, and her twin brother Mortimer, applaud the news that their dear friend, Mary Phillips, is embarking on her first engagement as a professional actress. Joining a touring company in the cast of Oscar Wilde's The Importance of Being Earnest, Mary is both intrigued and thrilled by her new life, until the sudden disappearance of fellow actress, Cynthia Grant. When Verity takes Cynthia's place in the cast, she sets out to discover what lies behind Cynthia's decision to abandon the play, calling on the services of dogged private investigator, George Benson. Soon they find themselves entangled in a web of murder, blackmail and kidnapping; threatened by some of the most feared denizens of the Victorian underworld.

As the nineteenth century draws to a close, a grateful nation prepares to celebrate its sovereign's long reign. Meanwhile, a traitor at the heart of the establishment is working in the interests of a foreign power to shake the very foundations of the British Empire and Verity Mallard and private detective George Benson soon find themselves enmeshed in the machinations of hostile forces. While Irish revolutionaries and agents of Imperial Germany pursue twin plots to strike at the pinnacle of the British state, Verity and George team up once again in a race against time to protect the realm. The thrilling third instalment of the Mallard Melodramas.