By using a logarithmic transformation, we will explore how
diffusion and random velocity processes enable to construct to
solvable discrete velocity Boltzmann equations and non-linear
reaction diffusion processes which are natural generalizations of the
Burgers' equation. Not only relevant for statistical physics, the
resulting parabolic and hyperbolic non-linear field equations will
be shown to be interpretable in terms of optimal stochastic control
problems.


[Invited by Prof. Christian Mazza]