Asymptotic behavior of oscillatory fractional processes

Renaud Marty (1) , Knut Solna (2)

1 IECN - Institut Élie Cartan de Nancy
2 Department of Mathematics [Irvine]

In this paper we consider the antiderivative of the product of a fractional random process and a periodic function. We establish that the rescaled process constructed in this way converges to a Brownian motion whose variance depends on the frequency of the periodic function and the Hurst parameter. We also prove that for two different frequencies the limits are independent. Finally, we discuss applications to wave propagation in random media.

Domaines: Probabilités [math.PR]

Renaud Marty, Knut Solna. Asymptotic behavior of oscillatory fractional processes. Lecture Notes in Mathematics, 2012, Séminaire de Probabilités XLIV, 2046, pp.247-269. ⟨hal-00558967⟩