Fractional Randomness and the Brownian Bridge
| Autor: | Charles S. Tapiero, Pierre Vallois |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Uniform distribution (continuous) Exponential distribution Fractional Brownian motion 010102 general mathematics Statistical and Nonlinear Physics Brownian bridge Covariance 01 natural sciences Fractional calculus 010101 applied mathematics Statistical physics 0101 mathematics Randomness Mathematics Central limit theorem |
| Zdroj: | Physica A: Statistical Mechanics and its Applications. 503:835-843 |
| ISSN: | 0378-4371 |
| DOI: | 10.1016/j.physa.2018.02.097 |
| Popis: | This paper introduces a statistical approach to fractional randomness based on the Central Limit Theorem. We show under general conditions that fractional noise-randomness defined relative to a uniform distribution, implies as well a fractional Brownian Bridge randomness rather than a Fractional Brownian Motion. We analyze further their fractional properties, namely, their variance and covariance and obtain specific results for particular distributions including the fractional uniform distribution and an exponential distribution. The results we obtain have both practical and theoretical implications to the many applications of fractional calculus and in particular, when they are applied to modeling statistical problems where time scaling and randomness prime. This is the case in finance, insurance and risk models as well as in other areas of interest. |
| Databáze: | OpenAIRE |
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