Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Series solution to the first-passage-time problem of a Brownian motion
  with an exponential time-dependent drift   We derive the first-passage-time statistics of a Brownian motion driven by an
exponential time-dependent drift up to a threshold. This process corresponds to
the signal integration in a simple neuronal model supplemented with an
adaptation-like current and reaching the threshold for the first time
represents the condition for declaring a spike. Based on the backward
Fokker-Planck formulation, we consider the survival probability of this process
in a domain restricted by an absorbent boundary. The solution is given as an
expansion in terms of the intensity of the time-dependent drift, which results
in an infinite set of recurrence equations. We explicitly obtain the complete
solution by solving each term in the expansion in a recursive scheme. From the
survival probability, we evaluate the first-passage-time statistics, which
itself preserves the series structure. We then compare theoretical results with
data extracted from numerical simulations of the associated dynamical system,
and show that the analytical description is appropriate whenever the series is
truncated in an adequate order.

14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics