Weak solution of stochastic differential equations with fractional diffusion coefficient

In stochastic financial and biological models, the diffusion coefficients often involve the term , or more general |x|(r), r (0, 1). These coefficients do not satisfy the local Lipschitz condition, which implies that the existence and uniqueness of the solution cannot be obtained by the standard conditions. This article establishes the existence of the weak solution for this class of stochastic differential equations by using the martingale representation and weak convergence methods.