Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of Integral Functionals of One-Dimensional Diffusions   In this expository paper we describe the pathwise behaviour of the integral
functional $\int_0^t f(Y_u)\,\dd u$ for any $t\in[0,\zeta]$, where $\zeta$ is
(a possibly infinite) exit time of a one-dimensional diffusion process $Y$ from
its state space, $f$ is a nonnegative Borel measurable function and the
coefficients of the SDE solved by $Y$ are only required to satisfy weak local
integrability conditions. Two proofs of the deterministic characterisation of
the convergence of such functionals are given: the problem is reduced in two
different ways to certain path properties of Brownian motion where either the
Williams theorem and the theory of Bessel processes or the first Ray-Knight
theorem can be applied to prove the characterisation.

31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin