On the Mixed Fractional Brownian Motion

  title={On the Mixed Fractional Brownian Motion},
  author={M. Zili},
If H = 1/2, BH is the ordinary Brownian motion denoted by B = {Bt, t ≥ 0}. Among the properties of this process, we recall the following: (i) B 0 = 0P-almost surely; (ii) for all t ≥ 0, E((B t )2)= t2H ; (iii) the increments of BH are stationary and self-similar with order H ; (iv) the trajectories of BH are almost surely continuous and not differentiable (see [7]). Let us take a and b as two real constants such that (a,b) = (0,0). 

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