Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Prophet inequalities for i.i.d. random variables with random arrival
  times   Suppose $X_1,X_2,...$ are i.i.d. nonnegative random variables with finite
expectation, and for each $k$, $X_k$ is observed at the $k$-th arrival time
$S_k$ of a Poisson process with unit rate which is independent of the sequence
$\{X_k\}$. For $t>0$, comparisons are made between the expected maximum
$M(t):=\rE[\max_{k\geq 1} X_k \sI(S_k\leq t)]$ and the optimal stopping value
$V(t):=\sup_{\tau\in\TT}\sE[X_\tau \sI(S_\tau\leq t)]$, where $\TT$ is the set
of all $\NN$-valued random variables $\tau$ such that $\{\tau=i\}$ is
measurable with respect to the $\sigma$-algebra generated by
$(X_1,S_1),...,(X_i,S_i)$. For instance, it is shown that $M(t)/V(t)\leq
1+\alpha_0$, where $\alpha_0\doteq 0.34149$ satisfies $\int_0^1(y-y\ln
y+\alpha_0)^{-1} dy=1$; and this bound is asymptotically sharp as $t\to\infty$.
Another result is that $M(t)/V(t)<2-(1-e^{-t})/t$, and this bound is
asymptotically sharp as $t\downarrow 0$. Upper bounds for the difference
$M(t)-V(t)$ are also given, under the additional assumption that the $X_k$ are
bounded.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
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
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int