论文标题
具有耗散漂移的传输方程的扩散近似
Diffusion Approximation for Transport Equations with Dissipative Drifts
论文作者
论文摘要
我们研究了具有小扰动参数的随机微分方程（SDE）。在漂移系数和局部Lipschitz的耗散状态下，在漂移和扩散系数上，我们证明了扰动的SDE的存在和唯一性，这也是扰动系统对未扰动系统的解决方案的解决方案的求解的趋同结果。当攻击参数接近时，我们考虑了以下问题。
We study stochastic differential equations(SDEs) with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence and uniqueness result for the perturbed SDE, also the convergence result for the solution of the perturbed system to the solution of the unperturbed system when the perturbation parameter approaches zero.We consider the application of the above-mentioned results to the Cauchy problem and the transport equations.
