Existence of Weak Solutions of Stochastic Differential Equations with Discontinuous Coefficients and with a Partially Degenerate Diffusion Operator

摘要

We study the existence of weak solutions of stochastic differential equations dX(t)=f(t,X(t))dt+g(t,X(t)dW(t), X∈Rd, (1)with Borel measurable functions f : R+ x Rd → Rd and g : R+ x Rd → Rdxd, where W(t) is a d-dimensional Brownian motion.