Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The first-crossing area of a diffusion process with jumps over a
  constant barrier   For a given barrier $S$ and a one-dimensional jump-diffusion process $X(t),$
starting from $x<S,$ we study the probability distribution of the integral
$A_S(x)= \int_0 ^ {\tau_S(x)}X(t) \ dt$ determined by $X(t)$ till its
first-crossing time $\tau_S(x)$ over $S.$ In particular, we show that the
Laplace transform and the moments of $A_S(x)$ are solutions to certain partial
differential-difference equations with outer conditions. The distribution of
the minimum of $X(t)$ in $[0, \tau_S(x)]$ is also studied. Thus, we extend the
results of a previous paper by the author, concerning the area swept out by
$X(t)$ till its first-passage below zero. Some explicit examples are reported,
regarding diffusions with and without jumps.

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The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph