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Approximation in law to the \(d\)-parameter fractional Brownian sheet based on the functional invariance principle. (English) Zbl 1102.60028

The authors give a results of convergence in law to the \(d\)-parameter fractional Brownian sheet. The approximations are a family of continuous processes constructed by using the functional invariance principle.

MSC:

60F17 Functional limit theorems; invariance principles
60G15 Gaussian processes
60G60 Random fields
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References:

[1] Al‘ os, E., Mazet, O., Nualart, D.: Stochastic calculus with respect to Gaussian processes. Ann. Probab. 29 (2001), no. 2, 766-801. · Zbl 1015.60047
[2] Bardina, X., Jolis, M., Tudor, C. A.: Convergence in law to the multi- ple fractional integral. Stochastic Process. Appl. 105 (2003), no. 2, 315-344. · Zbl 1075.60533
[3] Bardina, X., Jolis, M., Tudor, C. A.: Weak convergence to the frac- tional Brownian sheet and other two-parameter Gaussian processes. Statist. Probab. Lett. 65 (2003), no. 4, 317-329. · Zbl 1116.60328
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