论文标题
在Lyapunov条件下，在Kolmogorov方程中定期保存非左杆菌系数
Regularity preservation in Kolmogorov equations for non-Lipschitz coefficients under Lyapunov conditions
论文作者
论文摘要
鉴于全球Lipschitz的连续性和在ITô方程中的系数，相关半群的可不同性，对Kolmogorov方程的两倍的溶液的存在以及数值近似值较弱的差异的结果是已知的结果。 In this work and against the counterexamples of Hairer et al.(2015), the drift and diffusion coefficients having Lipschitz constants that are $o(\log V)$ and $o(\sqrt{\log V})$ respectively for a function $V$ satisfying $(\partial_t + L)V\leq CV$ is shown to be a generalizing condition in place of global Lipschitz continuity for以上。
Given global Lipschitz continuity and differentiability of high enough order on the coefficients in Itô's equation, differentiability of associated semigroups, existence of twice differentiable solutions to Kolmogorov equations and weak convergence rates of numerical approximations are known results. In this work and against the counterexamples of Hairer et al.(2015), the drift and diffusion coefficients having Lipschitz constants that are $o(\log V)$ and $o(\sqrt{\log V})$ respectively for a function $V$ satisfying $(\partial_t + L)V\leq CV$ is shown to be a generalizing condition in place of global Lipschitz continuity for the above.
