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Key words: Long memory (Long range dependence), Fractional Brownian motion, Fractional Ornstein-Uhlenbeck process, Exponential process, Burkholder-Davis-Gundy inequalities..
Keywords : fractional Brownian motion, function series expansion, rate of convergence, Gamma-mixed Ornstein–Uhlenbeck process.. AMS subject classification:
Path transformations have proved useful in the study of Brownian motion and related pro- cesses, by providing simple constructions of various conditioned processes such as
Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Itô integral with respect to a Brownian
the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when H = 1/2..
Keywords: time-change, inverse subordinator, Gaussian process, Fokker–Planck equation, Kol- mogorov equation, fractional Brownian motion, time-dependent Hurst parameter, Volterra
We prove here (by showing convergence of Chen’s series) that linear stochastic differential equa- tions driven by analytic fractional Brownian motion [6, 7] with arbitrary Hurst index
We define a Fractional Brownian Motion indexed by a sphere, or more generally by a compact rank one symmetric space, and prove that it exists if, and only if, 0 < H ≤ 1 / 2..
