Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimating a Random Walk First-Passage Time from Noisy or Delayed
  Observations   A random walk (or a Wiener process), possibly with drift, is observed in a
noisy or delayed fashion. The problem considered in this paper is to estimate
the first time \tau the random walk reaches a given level. Specifically, the
p-moment (p\geq 1) optimization problem \inf_\eta \ex|\eta-\tau|^p is
investigated where the infimum is taken over the set of stopping times that are
defined on the observation process.
  When there is no drift, optimal stopping rules are characterized for both
types of observations. When there is a drift, upper and lower bounds on
\inf_\eta \ex|\eta-\tau|^p are established for both types of observations. The
bounds are tight in the large-level regime for noisy observations and in the
large-level-large-delay regime for delayed observations. Noteworthy, for noisy
observations there exists an asymptotically optimal stopping rule that is a
function of a single observation.
  Simulation results are provided that corroborate the validity of the results
for non-asymptotic settings.

25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio