One-Dimensional Stochastic Differential Equations with Singular and Degenerate Coefficients

Abstract

Xt = Xo 4/ a(Xt)dWt + / V?(X) p(dw) for t > 0, Jq JR where W is a one-dimensional Brownian motion, a is a function that is bounded between two positive constants, \x is a finite measure with |/x({w}) | 0 for all t. Although this second equation does not have a unique solution, it does have a unique solution if one restricts attention to those solutions that spend zero time at 0.