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A process very similar to multifractional Brownian motion
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ayache, Antoine Bertrand, Pierre Raphael |
| Copyright Year | 2009 |
| Abstract | In [AT05], the multifractional Brownian (mBm) motion is obtained by replacing the constant parameter H of the fractional Brownian motion (fBm) by a smooth enough functional parameter H(.) depending on the time t. Here, we consider the process Z obtained by replacing in the wavelet expansion of the fBm the index H by a function H(.) depending on the dyadic point k/2 . This process was introduced in [BBCI00] to model fBm with piece-wise constant Hurst index and continuous paths. In this work, we investigate the case where the functional parameter satisfies an uniform Hölder condition of order β > sup t∈IR H(t) and ones shows that, in this case, the process Z is very similar to the mBm in the following senses: i) the difference between Z and a mBm satisfies an uniform Hölder condition of order d > sup t∈IR H(t); ii) as a by product, one deduces that at each point t ∈ IR the pointwise Hölder exponent of Z is H(t) and that Z is tangent to a fBm with Hurst parameter H(t). |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/0901.2808v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Brownian motion Dyadic transformation Esthesia Hurst exponent Population Parameter Wavelet |
| Content Type | Text |
| Resource Type | Article |
