Abstract:
Let us consider a Markov process with an infinitesimal operator
\begin{equation}
A_t=A^i(t,x)\frac{\partial}{\partial x^i } +B^{ij}(t,x)\frac{\partial^2}{\partial x^i\partial x^j}
\label{eq*}
\tag{*}
\end{equation}
where $x=(x^1,\dots,x^n )$ is a point in Riemann space $V_n$ with a metric $g_{ij}(t,x)$.
The necessary and sufficient conditions for the existence of transformation $x^{i'}=x^{i'}(t,x^1,\dots,x^n)$ which transforms the operator \eqref{eq*} into the well-known operator $$A_t^0=B^{i'j'}(t)\frac{\partial^2}{\partial x^{i'} \partial x^{j'}}$$ are given.
At the end of the paper an example is, given from statistics, in which these conditions are applied for establishing the density of the probabilities $f(t,x,\tau,\xi)$ of a certain Markov process.
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