A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stoc...(展开全部)

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stoc...(展开全部)

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introd...(展开全部)

From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zurich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites...(展开全部)

From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zurich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites...(展开全部)

This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough...(展开全部)

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering. Self-contained and unified in prese...(展开全部)

This book provides a concise introduction to stochastic calculus with some of its applications in mathematical finance, engineering and the sciences. Applications in finance include pricing of financial derivatives, such as options on stocks, exotic options and interest rate options. The filtering problem and its solution is presented as an application in engineering. Populatio...(展开全部)