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

Stochastic derivative and heat type PDEs