On It\^o differential equation in rough path theory
Probability
2013-11-04 v2
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(\beta) for \beta > 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.
Keywords
Cite
@article{arxiv.1306.2589,
title = {On It\^o differential equation in rough path theory},
author = {Terry J. Lyons and Danyu Yang},
journal= {arXiv preprint arXiv:1306.2589},
year = {2013}
}