论文标题
分数型螺旋螺旋ross过程的概括
Generalisation of Fractional-Cox-Ingersoll-Ross Process
论文作者
论文摘要
在本文中，我们将广义分数Cox-Ingersoll过程定义为奇异随机微分方程的正方形，相对于hurst参数h（0,1）和连续漂移函数，布朗运动的平方正方形。首先，我们表明，这种微分方程具有独特的解决方案，直到首次访问零时，它是连续且积极的。此外，我们证明，对于H> 1/2，几乎肯定到处都是积极的。在H <1/2的情况下，我们考虑了一系列增加功能的序列，并且证明击中零的概率趋于零，因为N到达无穷大。使用扩展的Cox-Ingersoll-Ross过程的概括，通过一些模拟来说明这些结果。
In this paper, we define a generalised fractional Cox-Ingersoll-Ross process as a square of singular stochastic differential equation with respect to fractional Brownian motion with Hurst parameter H in (0,1) and continuous drift function. Firstly, we show that this differential equation has a unique solution which is continuous and positive up to the time of the first visit to zero. In addition, we prove that it is strictly positive everywhere almost surely for H > 1/2. In the case where H < 1/2, we consider a sequence of increasing functions and we prove that the probability of hitting zero tends to zero as n goes to infinity. These results are illustrated with some simulations using the generalisation of the extended Cox-Ingersoll-Ross process.
