Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branching in a Markovian Environment   A branching process in a Markovian environment consists of an irreducible
Markov chain on a set of "environments" together with an offspring distribution
for each environment. At each time step the chain transitions to a new random
environment, and one individual is replaced by a random number of offspring
whose distribution depends on the new environment. We give a first moment
condition that determines whether this process survives forever with positive
probability. On the event of survival we prove a law of large numbers and a
central limit theorem for the population size. We also define a matrix-valued
generating function for which the extinction matrix (whose entries are the
probability of extinction in state j given that the initial state is i) is a
fixed point, and we prove that iterates of the generating function starting
with the zero matrix converge to the extinction matrix.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph