Fractional Randomness and the Brownian Bridge

Charles S. Tapiero and Pierre Vallois

Physica A: Statistical Mechanics and its Applications, 2018, vol. 503, issue C, 835-843

Abstract: 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.

Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437118301833
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:503:y:2018:i:c:p:835-843

DOI: 10.1016/j.physa.2018.02.097

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().