Fractional martingales and characterization of the fractional Brownian motion
نویسندگان
چکیده
In this paper we introduce the notion of α-martingale as the fractional derivative of order α of a continuous local martingale, where α ∈ (−12 , 1 2), and we show that it has a nonzero finite variation of order 2 1+2α , under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Lévy’s characterization theorem for the fractional Brownian motion.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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