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Recovering the pathwise Itô solution from averaged Stratonovich solutions

Abstract:

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 w...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Publisher copy:
10.1214/16-ECP3795

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Institution:
University of Oxford
Division:
Social Sciences Division
Department:
Divisional Administration; -man Institute; Mathematical Institute
Oxford college:
St Annes College
More by this author
Institution:
University of Oxford
Division:
Social Sciences Division
Department:
Divisional Administration; -man Institute; Mathematical Institute
Oxford college:
Balliol College
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Electronic Communications in Probability Journal website
Publication date:
2016-02-05
Acceptance date:
2015-08-10
DOI:
ISSN:
1083-589X
Pubs id:
pubs:720219
URN:
uri:d1eeae3c-ff31-4cc2-87c8-39397a276c68
UUID:
uuid:d1eeae3c-ff31-4cc2-87c8-39397a276c68
Local pid:
pubs:720219

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