Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flows and stochastic Taylor series in Ito calculus   For stochastic systems driven by continuous semimartingales an explicit
formula for the logarithm of the Ito flow map is given. A similar formula is
also obtained for solutions of linear matrix-valued SDEs driven by arbitrary
semimartingales. The computation relies on the lift to quasi-shuffle algebras
of formulas involving products of Ito integrals of semimartingales. Whereas the
Chen-Strichartz formula computing the logarithm of the Stratonovich flow map is
classically expanded as a formal sum indexed by permutations, the analogous
formula in Ito calculus is naturally indexed by surjections. This reflects the
change of algebraic background involved in the transition between the two
integration theories.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th