Research objectives and content
This research project aims at deriving existence and uniqueness conditions for solutions to anticipating stochastic differential equations. Furthermore Markov properties of the solutions will be examined. Basically two methods will be used: the theory of enlargement of filtrations and spatial transformations. A tool for describing such transformations will be the approach of Russo and Vallois to stochastic integration.
Training content (objective, benefit and expected impact)
The research project is strongly based on the pathwise point of view of stochastic integration. This is a central feature in the approach of F. Russo (Paris XIII) and P.Vallois to stochastic calculus. Benefit is also expected from the cooperation with scientists of the university Paris XIII working on relevant fields such as Wiener analysis, infinite dimensional stochastic differential equations and Besov spaces.
Links with industry / industrial relevance (22)
Anticipating stochastic differential equations are likely to have some impact on the investigation of financial markets. F. Russo has regular contacts with banks.