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arXiv · 1306.2589

On Itô differential equation in rough path theory

Terry J. Lyons·Danyu Yang
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Abstract

The solution of rough differential equation, driven by the Itô 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 Itô signature of the solution of parallel stochastic differential equation. Moreover, the Itô solution can be recovered pathwisely by concatenating discounted Stratonovich solutions.

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Terry J. Lyons, Danyu Yang. 2013-11-01. On Itô differential equation in rough path theory. https://arxiv.org/abs/1306.2589

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