论文标题
综合布朗运动的持久性指数的渐近指数和分数集成的布朗运动
Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion
论文作者
论文摘要
我们考虑了集成分数布朗运动的持续性概率和分别与参数$ h（$）的分数集成的布朗运动。对于集成的布朗尼运动，我们讨论了莫尔组和霍克洛夫的猜想，并确定持久性指数的渐近行为为$ h \ to $ h \ to $ to $ to $ h至0 $，$ h \ to $ h \ to 1，$，这符合猜想。对于分数集成的布朗尼运动（也称为Riemann-Liouville进程），我们发现持久性指数的渐近行为为$ h \ to 0 $。
We consider the persistence probability for the integrated fractional Brownian motion and the fractionally integrated Brownian motion with parameter $H,$ respectively. For the integrated fractional Brownian motion, we discuss a conjecture of Molchan and Khokhlov and determine the asymptotic behavior of the persistence exponent as $H\to 0$ and $H\to 1,$ which is in accordance with the conjecture. For the fractionally integrated Brownian motion, also called Riemann-Liouville process, we find the asymptotic behavior of the persistence exponent as $H\to 0$.
