论文标题
带有奇异内核和Hölder连续系数的随机伏特拉方程加性功能的路径独立性
Path independence for the additive functionals of stochastic Volterra equations with singular kernels and Hölder continuous coefficients
论文作者
论文摘要
在本文中，我们关注的是带有奇异内核和Hölder连续系数的随机Volterra方程。我们首先通过使用Yamada-Watanabe方法来建立这些方程式的良好性。然后，我们旨在表征这些方程的加性功能的路径独立性。这里的主要挑战是，随机燃烧方程的解决方案不是半明星或马尔可夫过程，因此获得常规，半明星类型随机微分方程的现有技术不再适用。为了克服这一困难，我们将相关的随机燃烧方程与某些抛物线型随机偏微分方程的轻度配方联系起来，并进一步将我们先前的结果应用于随机演化方程的路径独立性，以获得所需的结果。最后，作为一个重要的应用，我们考虑了一类随机燃烧方程，其内核与分数布朗运动相关，并得出了添加函数的路径独立性。
In this paper, we are concerned with stochastic Volterra equations with singular kernels and Hölder continuous coefficients. We first establish the well-posedness of these equations by utilising the Yamada-Watanabe approach. Then, we aim to characterise the path-independence for additive functionals of these equations. The main challenge here is that the solutions of stochastic Volterra equations are not semimartingales nor Markov processes, thus the existing techniques for obtaining the path-independence of usual, semimartingale type stochastic differential equations are no longer applicable. To overcome this difficulty, we link the concerned stochastic Volterra equations to mild formulation of certain parabolic type stochastic partial differential equations, and further apply our previous results on the path-independence for stochastic evolution equations to get the desired result. Finally, as an important application, we consider a class of stochastic Volterra equations whose kernels are related with fractional Brownian motions and derive the path-independence of additive functionals for them.
