Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Master equations and the theory of stochastic path integrals   This review provides a pedagogic and self-contained introduction to master
equations and to their representation by path integrals. We discuss analytical
and numerical methods for the solution of master equations, keeping our focus
on methods that are applicable even when stochastic fluctuations are strong.
The reviewed methods include the generating function technique and the Poisson
representation, as well as novel ways of mapping the forward and backward
master equations onto linear partial differential equations (PDEs). Spectral
methods, WKB approximations, and a variational approach have been proposed for
the analysis of the PDE obeyed by the generating function. After outlining
these methods, we solve the derived PDEs in terms of two path integrals. The
path integrals provide distinct exact representations of the conditional
probability distribution solving the master equations. We exemplify both path
integrals in analysing elementary chemical reactions. Furthermore, we review a
method for the approximation of rare event probabilities and derive path
integral representations of Fokker-Planck equations. To make our review
accessible to a broad community, we have used the language of probability
theory rather than quantum (field) theory. The probabilistic structures
underpinning various technical concepts, such as coherent states, the
Doi-shift, and normal-ordered observables, are thereby made explicit.

12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn