Introduction to Malliavin Calculus

David Nualart is the Black-Babcock Distinguished Professor in the Department of Mathematics at the University of Kansas. He has published around 300 scientific articles in the field of probability and stochastic processes, and he is the author of the fundamental monograph The Malliavin Calculus and Related Topics (2005). He has served on the editorial board of leading journals in probability, and from 2006 to 2008 was the editor-in-chief of Electronic Communications in Probability. He was elected Fellow of the Institute of Mathematical Statistics in 1997 and he received the Higuchi Award on Basic Sciences in 2015. Eulàlia Nualart is Associate Professor at Universitat Pompeu Fabra, Barcelona and a Barcelona Graduate School of Economics (GSE) Affiliated Professor. She is also the Deputy Director of the Barcelona GSE Master Program in Economics. Her research interests include stochastic analysis, Malliavin calculus, fractional Brownian motion, and Lévy processes. She has publications in top journals such as Stochastic Processes and their Applications, Annals of Probability, and the Journal of Functional Analysis. In 2013 she was awarded a Marie Curie Career Integration Grant.

• Preface; 1. Brownian motion; 2. Stochastic calculus; 3. Derivative and divergence operators; 4. Wiener chaos; 5. Ornstein-Uhlenbeck semigroup; 6. Stochastic integral representations; 7. Study of densities; 8. Normal approximations; 9. Jump processes; 10. Malliavin calculus for jump processes I; 11. Malliavin calculus for jump processes II; Appendix A. Basics of stochastic processes; References; Index.

'This book is a delightful and self-contained introduction to stochastic and Malliavin calculus that will guide the graduate students in probability theory from the basics of the theory to the borders of contemporary research. It is a must read written by two globally recognized experts!' Fabrice Baudoin, University of Connecticut