论文标题
由布朗运动驱动的积分的riemann近似的渐近误差分布
Asymptotic error distribution for the Riemann approximation of integrals driven by fractional Brownian motion
论文作者
论文摘要
我们考虑了随机积分的riemann总和近似相对于索引$ h \ geq \ frac12 $的分数Browian运动。我们在第一和二阶显示这些方案的收敛性。如果$ h> \ frac34 $和标准的布朗尼运动，则第二种情况下在第二种情况下以限制获得的过程是随机积分。这些结果是在积分是“受控”过程的假设下获得的。我们提供了许多此类过程的示例
We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion of index $H\geq \frac12$. We show the convergence of these schemes at first and second order. The processes obtained in the limit in the second case are stochastic integrals with respect to the Rosenblatt process if $H >\frac34$ and the standard Brownian motion otherwise. These results are obtained under the assumption that the integrand is a `controlled' process. We provide many examples of such processes, in particular fractional semimartingales and multiple Wiener-Itô integrals
