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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
As an application, assume d ≥ 2, we prove that the intersection local time of two independent, d−dimensional subfractional Ornstein-Uhlenbeck process,XH and $\tilde{X}^H$, exists in L2 if and only if Hd<2.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we consider Ornstein-Uhlenbeck process dXtH =−XtH dt+ vdStH, X0H =x, driven by a subfractional Brownian motion S H .
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Key Findings & Data:We prove that the subfractional Ornstein-Uhlenbeck process XH 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,XH and $\tilde{X}^H$, exists in L2 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 dXtH =−XtH dt+ vdStH, X0H =x, driven by a subfractional Brownian motion S H . We prove that the subfractional Ornstein-Uhlenbeck process XH 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,XH and $\tilde{X}^H$, exists in L2 if and only if Hd<2.
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Cite This Article
ZHU, D., SHEN, G., YIN, X. (2022). Intersection local time of subfractional Ornstein-Uhlenbeck processes. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 4, 975–990. https://ajindex.com/articles/530273