Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large fluctuations and growth rates of linear Volterra summation
  equations   This paper concerns the asymptotic behaviour of solutions of a linear
convolution Volterra summation equation with an unbounded forcing term. In
particular, we suppose the kernel is summable and ascribe growth bounds to the
exogenous perturbation. If the forcing term grows at a geometric rate
asymptotically or is bounded by a geometric sequence, then the solution
(appropriately scaled) omits a convenient asymptotic representation. Moreover,
this representation is used to show that additional growth properties of the
perturbation are preserved in the solution. If the forcing term fluctuates
asymptotically, we prove that fluctuations of the same magnitude will be
present in the solution and we also connect the finiteness of time averages of
the solution with those of the perturbation. Our results, and corollaries
thereof, apply to stochastic as well as deterministic equations, and we
demonstrate this by studying some representative classes of examples. Finally,
we show that our theory can be extended to cover a class of nonlinear equations
via a straightforward linearisation argument.

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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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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: adap-org
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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: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph