  The tensor-structured parametric analysis (TPA) has been recently developed
for simulating and analysing stochastic behaviours of gene regulatory networks
[Liao et. al., 2015]. The method employs the Fokker-Planck approximation of the
chemical master equation, and uses the Quantized Tensor Train (QTT) format, as
a low-parametric tensor-structured representation of classical matrices and
vectors, to approximate the high-dimensional stationary probability
distribution. This paper presents a detailed error analysis of all
approximation steps of the TPA regarding validity and accuracy, including
modelling error, artificial boundary error, discretization error, tensor
rounding error, and algebraic error. The error analysis is illustrated using
computational examples, including the death-birth process and a 50-dimensional
isomerization reaction chain.
