As an application, assume d ≥ 2 , we prove that the intersection local time of two independent, d − dimensional subfractional Ornstein-Uhlenbeck process, X H and $\tilde{ X}^H$ , exists in L 2 if and only if Hd< 2 .
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we consider Ornstein-Uhlenbeck process d X t H = − X t H d t + v d S t H , X 0 H = x, driven by a subfractional Brownian motion S H .
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Key Findings & Data:We prove that the subfractional Ornstein-Uhlenbeck process X H is local nondeterministic and give some properties of this process.
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Conclusion & Impact:As an application, assume d ≥ 2 , we prove that the intersection local time of two independent, d − dimensional subfractional Ornstein-Uhlenbeck process, X H and $\tilde{ X}^H$ , exists in L 2 if and only if Hd< 2 .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:subfractional Brownian motion · Ornstein-Uhlenbeck process · intersection local time
Abstract
In this paper, we consider Ornstein-Uhlenbeck process d X t H = − X t H d t + v d S t H , X 0 H = x, driven by a subfractional Brownian motion S H . We prove that the subfractional Ornstein-Uhlenbeck process X H is local nondeterministic and give some properties of this process. As an application, assume d ≥ 2 , we prove that the intersection local time of two independent, d − dimensional subfractional Ornstein-Uhlenbeck process, X H and $\tilde{ X}^H$ , exists in L 2 if and only if Hd< 2 .
Yin, X., Shen, G., Zhu, D. (2015). Intersection local time of subfractional Ornstein-Uhlenbeck processes. Hacettepe Journal of Mathematics and Statistics, Volume: 44 Issue: 4. https://ajindex.com/articles/1403274