论文标题
关于当地时代的存在和规律性
On the existence and regularity of local times
论文作者
论文摘要
我们研究一般$ d $维的随机过程的本地时代的存在和规律性。我们为它们的存在和规律性提供了一般条件。为了强调我们的结果的贡献，我们表明它们包括各种突出的例子，以及其他解决方案，用于由分数布朗运动驱动的随机微分方程，在这种情况下，当地时间的行为尚未完全理解到现在，并且在随机分析文献中仍然是一个开放的问题。特别是，这完成了有关此类方程式的当地时间行为的图片，最重要的是包括高维度以及大型和小型Hurst参数。作为其他主要示例，我们还表明，通过使用我们的一般方法，人们可以很容易地覆盖并扩展一些最近在Rosenblatt过程的当地时间和高斯准螺旋螺旋中获得的结果。
We study the existence and regularity of local times for general $d$-dimensional stochastic processes. We give a general condition for their existence and regularity properties. To emphasize the contribution of our results, we show that they include various prominent examples, among others solutions to stochastic differential equations driven by fractional Brownian motion, where the behavior of the local time was not fully understood up to now and remained as an open problem in the stochastic analysis literature. In particular this completes the picture regarding the local time behavior of such equations, above all includes high dimensions and both large and small Hurst parameters. As other main examples, we also show that by using our general approach, one can quite easily cover and extend some recently obtained results on the local times of the Rosenblatt process and Gaussian quasi-helices.
