In this paper, we derive the existence and the uniqueness theorem for the mild solution of nonlinear stochastic differential equations dX=[AX+f(X)]dt+[BX+g(X)]dW in infinite dimensions under non-Lipschitzian condition by investigating the convergence of the successive approximation.
通过构造收敛的逼近列的方法给出了非李普希茨条件下无穷维随机微分方程dX=[AX+f(X)]dt+[BX+g(X)]dW的适度解的存在唯一性定理。
When Euler scheme was used to solve the scalar autonomous stochastic differential equations and both of the drift coefficient and diffusion coefficient satisfied the linear growth condition and global Lipschitz condition, it was shown that the convergence order of Euler was 0.
证明了欧拉法用于求解标量自治随机微分方程时 ,在方程的偏移系数和扩散系数均满足线性增长条件和全局李普希兹条件的情形下 ,当噪声为增加噪声和附加噪声时 ,欧拉法的收敛阶分别为 0 。