Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a Theory of Additive Eigenvectors   The standard approach in solving stochastic equations is eigenvector
decomposition. Using separation ansatz $P(i,t)=u(i)e^{\mu t}$ one obtains
standard equation for eigenvectors $Ku=\mu u$, where $K$ is the rate matrix of
the master equation. While universally accepted, the standard approach is not
the only possibility. Using additive separation ansatz $S(i,t)=W(i)-\nu t$ one
arrives at additive eigenvectors. Here we suggest a theory of such
eigenvectors. We argue that additive eigenvectors describe conditioned Markov
processes and derive corresponding equations. The formalism is applied to
one-dimensional stochastic process corresponding to the telegraph equation. We
derive differential equations for additive eigenvectors and explore their
properties. The proposed theory of additive eigenvectors provides a new
description of stochastic processes with peculiar properties.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg