Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of Local Supermartingales   We characterize the event of convergence of a local supermartingale.
Conditions are given in terms of its predictable characteristics and quadratic
variation. The notion of stationarily local integrability plays a key role.

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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin