  In this paper we address again the problem of the connection between
multitime Brownian sheet and heat type PDEs. The main results include: the
volumetric character of the solutions of the forward (backward) diffusion-like
PDEs; the forward mean value of a Brownian process as the solution of the
forward heat PDE; the backward mean value of a Brownian process as the solution
of the backward heat PDE; the multitime stochastic processes with volumetric
dependence; the stochastic partial derivative of a stochastic process with
respect to a multitime Wiener process; Hermite polynomials stochastic
processes; union of Tzitzeica hypersurfaces (constant level sets of multitime
stochastic processes with volumetric dependence). The original results permit
to extend the complete integrability theory to multitime stochastic
differential systems, using path independent curvilinear integrals and
volumetric dependence.
