Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher variations for free L\'evy processes   For a general free L\'evy process, we prove the existence of its higher
variation processes as limits in distribution, and identify the limits in terms
of the L\'evy-It\^o representation of the original process. For a general free
compound Poisson process, this convergence holds almost uniformly, This implies
joint convergence in distribution to a $k$-tuple of higher variation processes,
and so the existence of $k$-fold stochastic integrals as almost uniform limits.
If the existence of moments of all orders is assumed, the result holds for free
additive (not necessarily stationary) processes and more general approximants.
In the appendix we note relevant properties of symmetric polynomials in
non-commuting variables.

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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph