Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A necessary and sufficient condition for the convergence of the
  derivative martingale in a branching L\'evy process   A continuous-time particle system on the real line satisfying the branching
property and an exponential integrability condition is called a branching
L\'evy process, and its law is characterized by a triplet
$(\sigma^2,a,\Lambda)$. We obtain a necessary and sufficient condition for the
convergence of the derivative martingale of such a process to a non-trivial
limit in terms of $(\sigma^2,a,\Lambda)$. This extends previously known results
on branching Brownian motions and branching random walks. To obtain this
result, we rely on the spinal decomposition and establish a novel zero-one law
on the perpetual integrals of centred L\'evy processes conditioned to stay
positive.

5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio