Anticipative Girsanov Transformations and Skorohod Stochastic Differential Equations

This book presents a survey of some recent developments in an important subfield of the new subject of anticipative stochastic analysis. D. Nualart and E. Pardoux have developed into a practicable calculus the theory of stochastic integration of processes not necessarily adapted to the driving Wiener process. This leads to anticipative stochastic differential equations with Skorohod integral and to anticipative Girsanov transformations, both of which are studied in the present work. The anticipative Girsanov transformations constitute the main tool for tackling stochastic differential equations with Skorohod integral. However, Buckdahn does not restrict attention only to this aspect but also considers different types of anticipative transformations and derives sufficient conditions for their absolute continuity with respect to the Wiener measure. The stochastic differential equations with Skorohod integral are studied under random initial conditions as well as under random boundary conditions.