Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renewal-scaled solutions of the Kolmogorov forward equation for residual
  times   Let $N(\tau)$ be a renewal process for holding times $\{X_i\}_{k \ge 0}$
,where $\{X_k\}_{k\ge 1}$ are iid with density $p(x)$. If the associated
residual time $R(\tau)$ has a density $u(x,t)$, its Kolmogorov forward equation
is given by \begin{equation*} \partial_t u(x,t)-\partial_x u(x,t) = p(x)u(0,t),
\quad x,t \in [0, \infty), \end{equation*} with an initial holding time density
$u(x,0)=u_0(x)$. We derive a measure-valued solution formula for the density of
residual times after an expected number of renewals occur. Solutions under this
time scale are then shown to evolve continuously in the space of measures with
the weak topology for a wide variety of holding times.

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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph