Probabilistic Models of the Conservation and Balance Laws in Switching Regimes

Abstract

A probabilistic representation is constructed for classical solution to the Cauchy problem for system of semilinear parabolic equations such that the second order terms with different coefficients enter in diagonal way, while the lower order terms enter in nondiagonal way. The systems of this kind arise as mathematical models of the parabolic conservation and balance laws and as mathematical models of dynamical systems with switching regimes.