Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exponential functional of random walks   The aim of this paper is to investigate discrete approximations of the
exponential functional $\int_0^{\infty} \exp(B(t) - \nu t) \di t$ of Brownian
motion (which plays an important role in Asian options of financial
mathematics) by the help of simple, symmetric random walks. In some
applications the discrete model could be even more natural than the continuous
one. The properties of the discrete exponential functional are rather different
from the continuous one: typically its distribution is singular w.r.t. Lebesgue
measure, all of its positive integer moments are finite and they characterize
the distribution. On the other hand, using suitable random walk approximations
to Brownian motion, the resulting discrete exponential functionals converge
a.s. to the exponential functional of Brownian motion, hence their limit
distribution is the same as in the continuous case, namely, the one of the
reciprocal of a gamma random variable, so absolutely continuous w.r.t. Lebesgue
measure. This way we give a new, elementary proof for an earlier result by
Dufresne and Yor as well.

1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics