Open Access
2016 Recovering the pathwise Itô solution from averaged Stratonovich solutions
Terry Lyons, Danyu Yang
Electron. Commun. Probab. 21: 1-18 (2016). DOI: 10.1214/16-ECP3795


We recover the pathwise Itô solution (the solution to a rough differential equation driven by the Itô signature) by concatenating averaged Stratonovich solutions on small intervals and by letting the mesh of the partition in the approximations tend to zero. More specifically, on a fixed small interval, we consider two Stratonovich solutions: one is driven by the original process and the other is driven by the original process plus a selected independent noise. Then by taking the expectation with respect to the selected noise, we can recover the increment of the bracket process and so recover the leading order approximation of the Itô solution up to a small error. By concatenating averaged increments and by letting the mesh tend to zero, the error tends to zero and we recover the Itô solution.


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Terry Lyons. Danyu Yang. "Recovering the pathwise Itô solution from averaged Stratonovich solutions." Electron. Commun. Probab. 21 1 - 18, 2016.


Received: 14 September 2014; Accepted: 10 August 2015; Published: 2016
First available in Project Euclid: 5 February 2016

zbMATH: 1338.60148
MathSciNet: MR3485376
Digital Object Identifier: 10.1214/16-ECP3795

Primary: 60G17 , 60H10

Keywords: pathwise Itô solution , Rough paths theory , Stratonovich solution

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