Probabilistic representations of boundary layer expansions
Using probabilistic methods we treat the problem of asymptotic expansions for a class of semilinear elliptic equations depending upon a small parameter ε which degenerate to parabolic equations when ε becomes zero. The method depends upon the representation of the solution of the partial differential equation as the expected value of a functional of an Ito stochastic differential equation.
Unable to display preview. Download preview PDF.