Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Properties of the Dirichlet Green's function for linear diffusions on
  a half line   This paper is concerned with the study of Green's functions for one
dimensional diffusions with constant diffusion coefficient and linear time
inhomogeneous drift. It is well know that the whole line Green's function is
given by a Gaussian. Formulas for the Dirichlet Green's function on the half
line are only known in special cases. The main object of study in the paper is
the ratio of the Dirichlet to whole line Green's functions. Bounds, asymptotic
behavior in the limit as the diffusion coefficient vanishes, and a log
concavity result are obtained for this ratio.

8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio