论文标题
由Hölder噪声驱动的夹心SDES带有无限的漂移
Sandwiched SDEs with unbounded drift driven by Hölder noises
论文作者
论文摘要
我们研究一个随机微分方程，具有无限的漂移和一般的Hölder连续噪声。事实证明，相应的方程式具有独特的解，它取决于漂移的特定形状，要么保持在某些连续函数上方，要么具有连续的上限和下边界。在关于噪声的一些其他假设下，我们证明该解决方案具有所有订单的时刻。我们完成研究，为解决方案提供了数值方案。为了说明我们应用的结果和动机，我们建议两个随机波动率模型，我们认为这是CIR和CEV过程的概括。
We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of an arbitrary order. The corresponding equation turns out to have a unique solution that, depending on a particular shape of the drift, either stays above some continuous function or has continuous upper and lower bounds. Under some additional assumptions on the noise, we prove that the solution has moments of all orders. We complete the study providing a numerical scheme for the solution. As an illustration of our results and motivation for applications, we suggest two stochastic volatility models which we regard as generalizations of the CIR and CEV processes.
