Constructing general rough differential equations through flow approximations

In Ciotir and Rascanu [9] and Nie and Rascanu [27], the authors have proved a sufficient and necessary condition for the invariance of a closed subset of R d for a

If the coefficient of dg t does not depend on the control process, we are able to extend the situation known for ordinary differential equations, and to prove an existence theorem for

We prove that the Itô map, that is the map that gives the solution of a differential equation controlled by a rough path of finite p-variation with p ∈ [2, 3) is locally

Also, the notion of linear rough differential equa- tions leads to consider multiplicative functionals with values in Banach algebra more general than tensor algebra and to

To build the controlled rough path integral of Theorem 4.15, with the theory of regularity structures we need to give a meaning to the product between y and W ˙ , where W ˙ is

Stochastic partial differential equations: a rough paths view on weak solutions via Feynman–Kac.. Joscha Diehl (1) ,

Also, the notion of linear rough differential equations leads to consider multiplicative functionals with values in Banach algebras more general than tensor algebras and to

4.2. Freidlin-Wentzell large deviation theory for diffusion processes. All to- gether, theorem on the rough path interpretation of Stratonovich differential equations, Lyons’