多参数布朗运动驱动的随机微分方程解的存在性

Existence Results of Solutions to Stochastic Differential Equations Driven by Multi-Parameter Brownian Motions

给出了多参数布朗运动驱动的随机微分方程在飘逸系数满足非连续性条件和扩散系数满足某种非Lipschitz条件下解的存在性定理。为此,利用截断和罚则函数法给出了非Lipschitz条件下方程解的比较性定理。最后利用Lipschitz函数逼近的方法给出了连续性飘逸系数满足线性增长条件下解的存在性定理。

The first aim of this paper is to derive an existence theorem of solutions to stochastic differential equations driven by multi-parameter Brownian motions when the drift coefficient is not continuous and the diffusion coefficient satisfies some non-Lipschitz condition.In doing so,we first obtain a comparison result of the solutions under some non-Lipschitz conditions on the coefficients by means of truncation and penalization method.With the aid of approximation of function satisfying linear growth condition by means of a series of Lipschitz functions,we obtain another existence result