论文标题
关于规范$α$稳定的圆柱lévy过程的随机整合
Stochastic integration with respect to canonical $α$-stable cylindrical Lévy processes
论文作者
论文摘要
在这项工作中，我们介绍了一种关于对称$α$稳定的圆柱lévy过程的随机整合理论。由于$α$稳定的圆柱级lévy工艺不享受半明天的分解，因此我们的方法基于对降压增量的切线序列的分离不平等。这种方法使我们能够表征可预测的Hilbert-Schmidt运算符值的最大空间，这些过程可相对于$α$稳定的圆柱级别的lévy工艺整合，以收集所有可预测的过程，并在Bochner Space $ L^α$中使用路径。我们通过建立主导的收敛结果来证明开发理论的力量和鲁棒性，从而允许随机积分和极限的互换。
In this work, we introduce a theory of stochastic integration with respect to symmetric $α$-stable cylindrical Lévy processes. Since $α$-stable cylindrical Lévy processes do not enjoy a semi-martingale decomposition, our approach is based on a decoupling inequality for the tangent sequence of the Radonified increments. This approach enables us to characterise the largest space of predictable Hilbert-Schmidt operator-valued processes which are integrable with respect to an $α$-stable cylindrical Lévy process as the collection of all predictable processes with paths in the Bochner space $L^α$. We demonstrate the power and robustness of the developed theory by establishing a dominated convergence result allowing the interchange of the stochastic integral and limit.
