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 theSchrodinger 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 will be 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"

Bio-organic Chemistry has corne of age - the sign of this is the start of a new series of Lecture Notes that are the product and substrate of spreading this line of modern knowledge among graduate students and research workers in such fields as mechanistic biochemistry, bio mimetic organic chemistry, biotechnological application of enzymology, to name only a few examples of how many frontiers are opened and borders lifted - just at. the time when the demand for a'''Synthetic Biology" and "Molecular Biotechnology" is increasing - fields that have been neglected for (too) long a time by "classical" chemists in curricula and imagination. We hope that through this first volume, which pOints in the several directions mentioned above, the profile of the undertaking will become clear and that it will find resonance among the scientific community interested in the thoughtful application of chemical and physical con cepts to biochemical and molecular-biological problems."