  We propose a method for describing stationary Markov processes on the class
of ultrametric spaces $\mathbb{U}$ isometrically embeddable in the field
$\mathbb{Q}_{p}$ of $p$-adic numbers. This method is capable of reducing the
study of such processes to the investigation of processes on $\mathbb{Q}_{p}$.
Thereby the traditional machinery of $p$-adic mathematical physics can be
applied to calculate the characteristics of stationary Markov processes on such
spaces. The Cauchy problem for the Kolmogorov-Feller equation of a~stationary
Markov process on such spaces is shown as being reducible to the Cauchy problem
for a pseudo-differential equation on $\mathbb{Q}_{p}$ with
non-translation-invariant measure $m\left(x\right)d_{p}x$. The spectrum of the
pseudo-differential operator of the Kolmogorov-Feller equation on
$\mathbb{Q}_{p}$ with measure $m\left(x\right)d_{p}x$ is found. Orthonormal
basis of real valued functions for
$L^{2}\left(\mathbb{Q}_{p},m\left(x\right)d_{p}x\right)$ is constructed from
the eigenfunctions of this operator.
