Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adapted integral representations of random variables   We study integral representations of random variables with respect to general
H\"older continuous processes and with respect to two particular cases;
fractional Brownian motion and mixed fractional Brownian motion. We prove that
arbitrary random variable can be represented as an improper integral, and that
the stochastic integral can have any distribution. If in addition the random
variable is a final value of an adapted H\"older continuous process, then it
can be represented as a proper integral. It is also shown that in the
particular case of mixed fractional Brownian motion, any adapted random
variable can be represented as a proper integral.

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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys