Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long Memory and Financial Market Bubble Dynamics in Affine Stochastic
  Differential Equations with Average Functionals   In this paper we consider the growth, large fluctuations and memory
properties of an affine stochastic functional differential equation with an
average functional where the contributions of the average and instantaneous
terms are parameterised. An asymptotic analysis of the solution of this
equation is conducted for all values of the parameters of the equation. When
solutions are recurrent, we show that the autocovariance function of the
solution decays at a polynomial rate, even though the solution is
asymptotically equal to another asymptotically stationary process whose
autocovariance function decays exponentially. It is shown that when solutions
grow, they do so at either a polynomial or exponential rate in time depending
on the sign of a parameter of the model, modulo some exceptional parameter
sets. On these exceptional sets, solutions are recurrent on the real line with
large fluctuations consistent with the Law of the Iterated logarithm, or
exhibit subexponential yet superpolynomial growth.

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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas