Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic tails of sums of products of positive random variables
  bounded by one   In this paper we show under weak assumptions that for
$R\stackrel{d}{=}1+M_1+M_1M_2+\ldots$, where $P(M\in[0,1])=1$ and $M_i$ are
independent copies of $M$, we have $\ln P(R>x)\sim C\, x\ln P(M>1-\frac1x)$ as
$x\to\infty$. The constant $C$ is given explicitly and its value depends on the
rate of convergence of $\ln P(M>1-\frac1x)$. Random variable $R$ satisfies the
stochastic equation $R\stackrel{d}{=}1+MR$ with $M$ and $R$ independent, thus
this result fits into the study of tails of iterated random equations, or more
specifically, of perpetuities.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph