  This paper establishes the conditions of existence of a stationary solution
to the first order autoregressive equation on a plane as well as properties of
the stationarity solution. The first-order autoregressive model on a plane is
defined by the equation
  $X_{i,j} = a X_{i-1,j} + b X_{i,j-1} + c X_{i-1,j-1} + \epsilon_{i,j}.$
  A stationary solution $X$ to the equation exists if and only if $(1-a-b-c)
(1-a+b+c) (1+a-b+c) (1+a+b-c) > 0$. The stationary solution $X$ satisfies the
causality condition with respect to the white noise $\epsilon$ if and only if
$1-a-b-c>0$, $1-a+b+c>0$, $1+a-b+c>0$ and $1+a+b-c>0$. A sufficient condition
for X to be purely nondeterministic is provided.
  An explicit expression for the autocovariance function of $X$ at some points
is provided. With Yule-Walker equations, this allows to compute the
autocovariance function everywhere. In addition, all situations are described
where different parameters determine the same autocovariance function of $X$.
