Multiple sub-fractional integrals and some approximations
Multiple sub-fractional integrals and some approximations
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DOI：
10.1080/00036810801927971
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发表时间：
2008-03
影响因子：
1.1
通讯作者：
C. Tudor
中科院分区：
文献类型：
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作者：
C. Tudor
我们研究关于偶分数次布朗运动(也称为次分数布朗运动)的多重分数次积分。利用偶数分式布朗运动的表示式和传递原理，引入了关于布朗运动的Wiener积分的多重积分。然后，我们还考虑了多重Stratonovich分数次积分的Riemann-Stieltjes积分逼近。对于两种标准逼近(Wong-Zakai逼近和软化逼近)和连续被积，证明了这两种逼近对多重Stratonovich次分数次积分的一致范数的均方收敛.
We study multiple fractional integrals with respect to the even fractional Brownian motion (also called sub-fractional Brownian motion). The multiple integrals are introduced by using a representation formula for the even fractional Brownian motion as a Wiener integral with respect to a Brownian motion defined on the same probability space and a transfer principle. Then, Riemann–Stieltjes integral approximations to multiple Stratonovich fractional integrals are also considered. For two standard approximations (Wong–Zakai and mollifier approximations) and continuous integrands, the mean square convergence in the uniform norm of these approximations to the multiple Stratonovich sub-fractional integral is shown.