Weak solutions of stochastic differential equations with discontinuous coefficients (Q1603135)

Three different types of weak solutions of the vector stochastic differential equation \[ dx(t)= f(t, x(t)) dt+ g(t,x(t)) dW(t) \] with initial condition \(x(0)= x_0\) are defined. Theorems establishing the existence of the three types of weak solutions of this value problem are proved under less restrictive assumptions than usual. A theorem on the dependence of weak solutions of \(f\), \(g\) and the initial condition is proved.