Some Processes Associated with Fractional Bessel Processes
نویسندگان
چکیده
Let B = {(B1 t , . . . , Bd t ) , t ≥ 0} be a d-dimensional fractional Brownian motion with Hurst parameter H and let Rt = √ (B1 t ) 2 + · · · + (Bd t )2 be the fractional Bessel process. Itô’s formula for the fractional Brownian motion leads to the equation Rt = ∑d i=1 ∫ t 0 Bi s Rs dBi s + H(d − 1) ∫ t 0 s2H−1 Rs ds . In the Brownian motion case (H = 1/2), Xt = ∑d i=1 ∫ t 0 Bi s Rs dBi s is a Brownian motion. In this paper it is shown that Xt is not a fractional Brownian motion if H 6= 1/2. We will study some other properties of this stochastic process as well. Mathematics Subject Classification (2000): 60G15, 60G17, 60H05, 60H40.
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