Stochastic Integration by Parts and Functional Itô Calculus
Springer International Publishing (Verlag)
978-3-319-27127-9 (ISBN)
This volume contains lecture notes from the coursesgiven by Vlad Bally and Rama Cont at the Barcelona Summer School on StochasticAnalysis (July 2012).
The notes of the course by Vlad Bally, co-authoredwith Lucia Caramellino, develop integration by parts formulas in an abstractsetting, extending Malliavin's work on abstract Wiener spaces. The results areapplied to prove absolute continuity and regularity results of the density fora broad class of random processes.
Rama Cont's notes provide anintroduction to the Functional Itô Calculus, a non-anticipative functionalcalculus that extends the classical Itô calculus to path-dependent functionalsof stochastic processes. This calculus leads to a new class of path-dependentpartial differential equations, termed Functional Kolmogorov Equations, whicharise in the study of martingales and forward-backward stochastic differentialequations.This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to practitioners in mathematical finance.
Integration by parts formulas, Malliavin calculus and regularity of probability laws.- Functional Ito calculus and functional Kolmogorov equations.
| Erscheinungsdatum | 08.10.2016 |
|---|---|
| Reihe/Serie | Advanced Courses in Mathematics - CRM Barcelona |
| Zusatzinfo | IX, 208 p. 1 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 168 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | interpolation spaces • Kolmogorov equations • Malliavin calculus • mathematics and statistics • Ordinary differential equations • Partial differential equations • Path-dependent PDE • Probability laws • Probability theory and stochastic processes |
| ISBN-10 | 3-319-27127-X / 331927127X |
| ISBN-13 | 978-3-319-27127-9 / 9783319271279 |
| Zustand | Neuware |
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