Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First-passage Brownian functionals with stochastic resetting   We study the statistical properties of first-passage time functionals of a
one dimensional Brownian motion in the presence of stochastic resetting. A
first-passage functional is defined as $V=\int_0^{t_f} Z[x(\tau)]$ where $t_f$
is the first-passage time of a reset Brownian process $x(\tau)$, i.e., the
first time the process crosses zero. In here, the particle is reset to $x_R>0$
at a constant rate $r$ starting from $x_0>0$ and we focus on the following
functionals: (i) local time $T_{loc} = \int _0^{t_f}d \tau ~ \delta (x-x_R)$,
(ii) residence time $T_{res} = \int _0^{t_f} d \tau ~\theta (x-x_R)$, and (iii)
functionals of the form $A_n = \int _{0}^{t_f} d \tau [x(\tau)]^n $ with $n
>-2$. For first two functionals, we analytically derive the exact expressions
for the moments and distributions. Interestingly, the residence time moments
reach minima at some optimal resetting rates. A similar phenomena is also
observed for the moments of the functional $A_n$. Finally, we show that the
distribution of $A_n$ for large $A_n$ decays exponentially as $\sim
\text{exp}\left( -A_n/a_n\right)$ for all values of $n$ and the corresponding
decay length $a_n$ is also estimated. In particular, exact distribution for the
first passage time under resetting (which corresponds to the $n=0$ case) is
derived and shown to be exponential at large time limit in accordance with the
generic observation. This behavioural drift from the underlying process can be
understood as a ramification due to the resetting mechanism which curtails the
undesired long Brownian first passage trajectories and leads to an accelerated
completion. We confirm our results to high precision by numerical simulations.

29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg