EAN: 9783319271279

ADVANCED COURSES IN MATHEMATICS - CRM BARCELONA...

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.

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