论文标题
随机步行的限制，具有分布强大的过渡概率
Limits of random walks with distributionally robust transition probabilities
论文作者
论文摘要
我们考虑了一个非线性随机步行，在每个时间步骤中，可以自由选择其自身的过渡概率（W.R.T. Wasserstein距离）的过渡概率（W.R.T. Wasserstein距离）。与经典框架相比，我们表明，当通过缩放限制从离散时间到连续时间时，这种非线性随机步行会产生非线性的半群。我们明确地计算了该半群的生成器，并将对应的PDE作为初始Lévy过程的发电机的扰动。
We consider a nonlinear random walk which, in each time step, is free to choose its own transition probability within a neighborhood (w.r.t. Wasserstein distance) of the transition probability of a fixed Lévy process. In analogy to the classical framework we show that, when passing from discrete to continuous time via a scaling limit, this nonlinear random walk gives rise to a nonlinear semigroup. We explicitly compute the generator of this semigroup and corresponding PDE as a perturbation of the generator of the initial Lévy process.
