2017/01/05 by Peter Parczewski, Parczewski, Peter
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #60H05 #60H07 #65C30 #Advanced Queuing Theory Analysis #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1701.01312
openalex publication_date 2017/01/05 · openalex created_date 2022/09/19 · openalex updated_date 2026/07/28
We consider optimal approximation with respect to the mean square error of\nIt o integrals and Skorohod integrals given an equidistant discretization of\nthe Brownian motion. We obtain for suitable integrands optimal rates smaller\nthan the standard n-1, where n denotes the number of evaluations of the\nBrownian motion. For the It o integral this is due to the Weyl\nequidistribution theorem and discontinuities of the integrand. For the Skorohod\nintegral the situation is more complicated and relies on a reformulation of the\nWiener chaos expansion. Here, we specify conditions on the integrands to obtain\noptimal rates n-1/2, respectively, examples of lower rates.\n