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Introduction to Malliavin Calculus

Buch | Hardcover
246 Seiten
2018
Cambridge University Press (Verlag)
978-1-107-03912-4 (ISBN)
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This textbook offers a compact introduction to Malliavin calculus. It covers recent applications, and includes a self-contained presentation of preliminary material on Brownian motion and stochastic calculus. Accessible to non-experts, graduate students and researchers can use this book to master the core techniques necessary for further study.
This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.

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.

Erscheinungsdatum
Reihe/Serie Institute of Mathematical Statistics Textbooks
Verlagsort Cambridge
Sprache englisch
Maße 157 x 236 mm
Gewicht 460 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Wirtschaft Allgemeines / Lexika
Wirtschaft Betriebswirtschaft / Management Finanzierung
ISBN-10 1-107-03912-6 / 1107039126
ISBN-13 978-1-107-03912-4 / 9781107039124
Zustand Neuware
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