Application of quasi-Feynman formulae to a number of physical problems

In the report for one-dimensional diffusion equation with constant diffusion coefficient n-th power of the Chernoff function has been calculated explicitly. Interconnection of solutions of this equation obtained by means both quasi-Feynman formula and Green's function has been demonstrated. Behaviour of these solutions under stochastic initial condition has been discussed. The case of nongaussian initial condition has been considered too.