## The fractional mixed fractional Brownian motion.(English)Zbl 1065.60034

Let $$B_1$$ and $$B_2$$ be two independent fractional Brownian motions of Hurst index $$H_1$$ and $$H_2$$, respectively. Given real numbers $$\lambda_1$$ and $$\lambda_2$$, the two-parameter process $$Z$$ is defined by $Z(w,s):= \lambda_1\,s^{H_2}\,B_1(w) + \lambda_2\,s^{H_1}\,B_2(w),\quad 0\leq w\leq s.$ The investigated statistic is $$Y(t):= \sup_{0\leq s\leq t}\sup_{0\leq w\leq s}| Z(w,s)|$$. The main theorem of the present paper states necessary conditions for a function $$f$$ on $$[0,\infty)$$ in order to belong to the lower-lower class of $$Y$$.

### MSC:

 60G15 Gaussian processes 60G18 Self-similar stochastic processes
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### References:

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