Limits for weighted p-variations and likewise functionals of fractional diffusions with drift

José León and Carenne Ludeña

Stochastic Processes and their Applications, 2007, vol. 117, issue 3, 271-296

Abstract: Let Xt be the pathwise solution of a diffusion driven by a fractional Brownian motion with Hurst constant H>1/2 and diffusion coefficient [sigma](t,x). Consider the successive increments of this solution, [Delta]Xi=Xi/n-X(i-1)/n. Using a cylinder approximation for the solution Xt, our main result yields that if 1/2 [infinity] where W is a Wiener process which is independent of BH and CH,p is a constant which depends on H and on p. In the place of p-variations we may consider functions that satisfy an almost multiplicative structure such as even polynomials or polynomials of absolute values. By considering second order increments of the discrete sample Xi we obtain analogous results for the whole interval 1/2

Keywords: Fractional; Brownian; motion; p-variations; Fractional; diffusions (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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