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The inverse problem for rough controlled differential equations · arXivDesk

1407.2768Jul 10, 2014added section on rough path theory

The inverse problem for rough controlled differential equations

I. Bailleul, J. Diehl

Probability Classical Analysis and ODEs

Abstract

We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic filtering and statistics demonstrate the practical relevance of our result.

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We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic filtering and statistics demonstrate the practical relevance of our result.

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Researchers working in math.PR and adjacent areas.

Claims

The paper addresses: The inverse problem for rough controlled differential equations.
We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution.

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Author comment: added section on rough path theory

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