Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable distributions and pseudo-processes related to fractional Airy
  functions   In this paper we study pseudo-processes related to odd-order heat-type
equations composed with L\'evy stable subordinators. The aim of the article is
twofold. We first show that the pseudo-density of the subordinated
pseudo-process can be represented as an expectation of damped oscillations with
generalized gamma distributed parameters. This stochastic representation also
arises as the solution to a fractional diffusion equation, involving a
higher-order Riesz-Feller operator, which generalizes the odd-order heat-type
equation. We then prove that, if the stable subordinator has a suitable
exponent, the time-changed pseudo-process becomes a genuine L\'evy stable
process. This result permits us to obtain a power series representation for the
probability density function of an arbitrary asymmetric stable process of
exponent $\nu>1$ and skewness parameter $\beta$, with $0<|\beta|<1$. The
methods we use in order to carry out our analysis are based on the study of a
fractional Airy function which arises in the study of the higher-order
Riesz-Feller operator.

9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys