Stochastic analysis and conservation laws

Stochastic analysis is applied to a Cauchy problem for a scalar conservation law by using "vanishing viscosity" method . It is proved that the stochastic characteristic of equation converges to the characteristic of equation . In this way a well known result is recovered, that is, the solution of converges to the entropy solution of naturally. Entropy condition is crucial to the proofs. The result suggests that the new method, stochastic analysis, may be useful for solving difficult problems of quasi-linear partial differential