ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations
提出一种算法，能以任意预设误差界ε概率1地模拟分数布朗运动及其驱动的随机微分方程，支持误差界顺序更新，便于结合高级模拟技术高效估计泛函期望。
Consider a fractional Brownian motion (fBM) [Formula: see text] with Hurst index [Formula: see text]. We construct a probability space supporting both B H and a fully simulatable process [Formula: see text] such that[Formula: see text] with probability one for any user-specified error bound [Formula: see text]. When [Formula: see text], we further enhance our error guarantee to the α-Hölder norm for any [Formula: see text]. This enables us to extend our algorithm to the simulation of fBM-driven stochastic differential equations [Formula: see text]. Under mild regularity conditions on the drift and diffusion coefficients of Y, we construct a probability space supporting both Y and a fully simulatable process [Formula: see text] such that[Formula: see text] with probability one. Our algorithms enjoy the tolerance-enforcement feature, under which the error bounds can be updated sequentially in an efficient way. Thus, the algorithms can be readily combined with other advanced simulation techniques to estimate the expectations of functionals of fBMs efficiently.