Non-Lipschitz stochastic differential equations driven by multi-parameter brownian motions

By proving an extension of nonlinear Bihari's inequality (including Gronwall's inequality) to multi-parameter and non-Lebesgue measure, in this paper we first prove by successive approximation the existence and uniqueness of solution of stochastic differential equation with non-Lipschitz coefficients and driven by multi-parameter Brownian motion. Then we study two discretizing schemes for this type of equation, and obtain their L²-convergence speeds.