Stochastic Partial Differential Equations with Irregular Drift Coeffecients (completed)
This project is about the interplay between strong solutions to stochastic (partial) differential equations and the Malliavin Calculus.
About the project
The tradition when studying differential equations is that the solutions inherits properties from the coefficients. It turns out that in the case of stochastic differential equations, even if the coefficients are 'ugly', the solutions will be 'nice'. More specifically, the strong solutions are Malliavin differentiable even though the drift is discontinuous. This property also gives insight about the flow generated by the same equation.
The aim of the project is to develop a new method to construct strong solutions of stochastic partial differential equations with discontinuous drift. The starting point will be a compactness criterion based on Malliavin Calculus, and the primary objective is to show that such solutions are Malliavin differentiable. One can then proceed to consider the flow of these equations, since this is closely related to the Malliavin Calculus.
This gives rise to believe that there is an intrinsic connection between Malliavin Calculus and strong solutions, and that the technique is somehow close to the true nature of stochastic partial differential equations.
This project is financed by the Reseach Council of Norway (external link) under the FRIPRO scheme. Funding ID: 231633