论文标题
混合FBM和其他混合过程的持久性概率
Persistence probabilities of mixed FBM and other mixed processes
论文作者
论文摘要
我们考虑具有不同自相似性指数的两个自相似为中心的高斯过程的总和。在协方差函数的非负假设和一些进一步的次要条件下，我们表明，总和的持续性概率的渐近行为与具有更大的自相似性指数的单个过程相同。 特别是，这涵盖了Cheridito（2001）中引入的混合分数布朗尼运动，并表明相应的持久性概率在渐近上渐近地衰减，持久性指数$ 1- \ max（1/2，h），其中$ h $是下层布朗的hurst参数。
We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under non-negativity assumptions of covariance functions and some further minor conditions, we show that the asymptotic behaviour of the persistence probability of the sum is the same as for the single process with the greater self-similarity index. In particular, this covers the mixed fractional Brownian motion introduced in Cheridito (2001) and shows that the corresponding persistence probability decays asymptotically polynomially with persistence exponent $1-\max(1/2,H),$ where $H$ is the Hurst parameter of the underlying fractional Brownian motion.
