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2015 Approximating the Rosenblatt process by multiple Wiener integrals
Litan Yan, Yumiao Li, Di Wu
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Electron. Commun. Probab. 20: 1-16 (2015). DOI: 10.1214/ECP.v20-3517


Let $Z^{H}$ be the Rosenblatt process with the representation$$Z^H_t=\int_0^t\int_0^tL^H(t,s,r)dB_{s}dB_{r},$$where $B$ is a standard Brownian motion, $\frac12<H<1$ and $L^H$ is a given kernel. By reviewing the kernel $L^H$ we construct its approximation of multiple Wiener integrals of the form $$\int_{0}^{t}\int_{0}^{t}\left\{k_{1}(sr)^{-\frac{1}{2}H} +k_{2}(s\vee r)^{\frac{1}{2}H}(s\wedge r)^{-\frac{1}{2}H}|s-r|^{H-1}\right\}dB_{s}dB_{r}, \;\;k_1,k_2\geq 0.$$We find an optimal approximation of $Z^{H}$ via calculating accurately the values of $k_1,k_2$.


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Litan Yan. Yumiao Li. Di Wu. "Approximating the Rosenblatt process by multiple Wiener integrals." Electron. Commun. Probab. 20 1 - 16, 2015.


Accepted: 14 February 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1327.60112
MathSciNet: MR3314646
Digital Object Identifier: 10.1214/ECP.v20-3517

Primary: 60G18
Secondary: 60H05

Keywords: Multiple Wiener integrals , optimal approximation , Rosenblatt process

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