Transformation of Measure on Wiener Space

The notion of transformation of measure is of fundamental importance in Analysis and Probability Theory. In the context of Ite. calculus, the Gir sanov theorem elassified the structure of the Random-Nikodym derivative and turned out to be of fundamental importance for the development of Itö Calculus (its extension to martingales, the martingale problem, weak solu tions of stochastic differential equations) and its applications (e.g. filtering, stochastic control, and mathematical finance). This set up is associated with a time ftow and cannot be extended to cases such as stochastic partial differ n ential equations on subsets of IR , n > 1, wh ich lack the time ftow structure. The problem of transformation of measures for general structures started in the late forties with the work of Cameron and Martin. The work of Ramer in the mid-seventies and of Kusuoka in the early eighties elarified the structure of the (Radon-Nikodym) derivative in the general case and pointed out the importance of the Malliavin calculus to the furt her development of the the ory. We believe that the further development of stochastic analysis is elosely related to the topics discussed in this book.