  We consider the degenerate Einstein's Brownian motion model for the case when
the time interval ($\tau$) of particle Jumps before collision (free jumps)
reciprocal to the number of particles per unit volume $u(x,t) > 0$ at the point
of observation $x$ at time $t$. The parameter $0 < \tau \leq C < \infty$,
controls characteristic of the fluid "almost decreases" to $ 0 $ when $u
\rightarrow \infty$. This degeneration leads to the localisation of the spread
of particle propagation in the media. In our report we will present a
structural condition of the time interval of free jumps - $\tau$ and the
frequency of these free jumps $\phi$ as functions of $u$ which guarantees the
finite speed of propagation of $u$.
