论文标题
用于提取退化扩散的唯一捕获者弱解决方案的选择程序
A selection procedure for extracting the unique Feller weak solution of degenerate diffusions
论文作者
论文摘要
在这项工作中，我们表明，对于一类具有有限的连续漂移和扩散系数的退化扩散的问题，非分类近似值的噪声极限会导致独特的feller极限。该证明使用应用于相关的向后kolmogorov方程的粘度解决方案理论。在漂移和扩散系数的适当条件下，我们将建立一个比较原理，并且在fly虫解决方案与相关的Kolmogorov方程的连续粘度解之间建立一个对应关系。这项工作可以被认为是V. S. Borkar和K. S. Kumar（2010）的工作的扩展。
In this work, we show that for the martingale problem for a class of degenerate diffusions with bounded continuous drift and diffusion coefficients, the small noise limit of non-degenerate approximations leads to a unique Feller limit. The proof uses the theory of viscosity solutions applied to the associated backward Kolmogorov equations. Under appropriate conditions on drift and diffusion coefficients, we will establish a comparison principle and a one-one correspondence between Feller solutions to the martingale problem and continuous viscosity solutions of the associated Kolmogorov equation. This work can be considered as an extension to the work of V. S. Borkar and K. S. Kumar (2010).
