Existence of weak solutions of stochastic differential equations with discontinuous coefficients and with a partially degenerate diffusion operator (Q1033625)

The authors studies the existence of weak solutions of stochastic differential equations \(dX(t) = f(t,X(t))dt + g(t,X(t))dW(t), \quad X \in \mathbb{R}^d\), with Borel measurable functions, \(f : \mathbb{R}_+ \times \mathbb{R}^d \to \mathbb{R}^d\) and \( g: \mathbb{R}_+ \times \mathbb{R}^d \to \mathbb{R}^{d \times d}\), where \(W(t)\) is a \(d\)-dimensional Brownian motion. A well known result states that there exist a weak solution if \(f,g\) are continuous and bounded. The aim of this paper is to relax the conditions on the functions \(f,g\) in order to obtain the existence of weak solutions.