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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
(f) A possible reason why sub-fractional Brownian motion is the limit in the non-branching model with deterministic θ (Remark 2.3(a)) and in the branching model (Theorem 2.4(a)) is
Key words: Curvilinear integrals, H¨older continuity, rough paths, stochastic integrals, stochastic differential equations, fractional Brownian motion.. AMS 2000 Subject
Keywords : fractional Brownian motion, function series expansion, rate of convergence, Gamma-mixed Ornstein–Uhlenbeck process.. AMS subject classification:
Key words: stochastic differential equations, Brownian motion, Law of the Iterated Logarithm, Motoo’s theorem, stochastic comparison principle, stationary processes,
Keywords Wiener space, Sobolev space, Stochastic integral, Fractional Brownian Motion, Itˆ o’s formula.. AMS Subject Classification (1991)
Keywords: time-change, inverse subordinator, Gaussian process, Fokker–Planck equation, Kol- mogorov equation, fractional Brownian motion, time-dependent Hurst parameter, Volterra
Instead to use here the Langevin equation, we use the more tractable Airault–Malliavin equation, that represents infinite dimen- sional Brownian motion on a current group.. 2 A
