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Keywords: g –expectation, G –expectation, G –normal distribution, BSDE, SDE, nonlinear probability theory, nonlinear expectation, Brownian motion, Itˆo’s stochastic calculus,
To solve fractional differential equations without delay, the second main tool would be to define the integral of a weakly controlled path with respect to fractional Brownian motion
The boundary dimension of B [0 , 1] is the Hausdorff dimension of the “frontier” of Brownian motion, where the frontier of planar Brownian motion is t he boundary of the un-
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:
In a first step, we show that the small deviation problem of processes that are subordinated to Brownian motion (or more generally, to a strictly β -stable Lévy process) are
We then consider generalized quadratic variations of Gaussian fields with stationary increments under the assumption that their spectral density is asymptotically self-similar and
Keywords: Gaussian random walk; maximum; Riemann zeta function; Euler-Maclaurin summa- tion; equidistant sampling of Brownian motion; finite
