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- W4367365506 abstract "We study how to construct a stochastic process on a finite interval with given `roughness' and finite joint moments of marginal distributions. Our construction method is based on Schauder representation along a general sequence of partitions and has two ramifications. We show that the variation index of a process along a given partition sequence (the infimum value $p$ such that the $p$-th variation is finite) may not be equal to the reciprocal of Holder exponent, and provide a pathwise estimator of Holder exponent. Moreover, we construct a non-Gaussian family of stochastic processes which are statistically indistinguishable from (fractional) Brownian motions. Therefore, when observing a sample path from a process in a financial market such as a price or volatility process, we should not measure its Holder roughness by computing $p$-th variation and should not conclude that the sample is from Brownian motion or fractional Brownian motion even though it exhibits the same properties of those Gaussian processes." @default.
- W4367365506 created "2023-04-30" @default.
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- W4367365506 date "2023-04-26" @default.
- W4367365506 modified "2023-10-01" @default.
- W4367365506 title "Applications of Schauder-type basis: estimating Holder exponent, fake fractional Brownian motion" @default.
- W4367365506 doi "https://doi.org/10.48550/arxiv.2304.13794" @default.
- W4367365506 hasPublicationYear "2023" @default.
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