A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm
2014 ◽
Vol 51
(1)
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pp. 1-18
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Keyword(s):
We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.
2014 ◽
Vol 51
(01)
◽
pp. 1-18
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2017 ◽
Vol 54
(2)
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pp. 444-461
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Keyword(s):
1996 ◽
Vol 348
(8)
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pp. 3193-3213
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Keyword(s):
2019 ◽
Vol 33
(3)
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pp. 1691-1714
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2020 ◽
Vol 130
(5)
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pp. 2675-2692
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