Probabilistic Interpretation of the Vanishing Viscosity Method for Systems of Conservation and Balance Laws

Systems of nonlinear parabolic equations with small parameter multiplying the highest derivative and stochastic models associated with them are considered. It is shown that the vanishing viscosity method, which makes it possible to choose physical solutions to the Cauchy problem for systems of nonlinear conservation laws, has a natural justification in terms of stochastic models. A similar result for balance laws is also obtained.