On It\o differential equation in rough path theory
Abstract
The solution of rough differential equation, driven by the It\o signature of a continuous local martingale, exists uniquely a.s. when the vector field is Lip(β) for β > 1, and coincides a.s. with the It\o signature of the solution of parallel stochastic differential equation. Moreover, the It\o solution can be recovered pathwisely by concatenating discounted Stratonovich solutions.
0