EconPapers    
Economics at your fingertips  
 

A class of micropulses and antipersistent fractional Brownian motion

R. Cioczek-Georges and Benoît Mandelbrot

Stochastic Processes and their Applications, 1995, vol. 60, issue 1, 1-18

Abstract: We begin with stochastic processes obtained as sums of "up-and-down" pulses with random moments of birth [tau] and random lifetime w determined by a Poisson random measure. When the pulse amplitude [var epsilon] --> 0, while the pulse density [delta] increases to infinity, one obtains a process of "fractal sum of micropulses." A CLT style argument shows convergence in the sense of finite dimensional distributions to a Gaussian process with negatively correlated increments. In the most interesting case the limit is fractional Brownian motion (FBM), a self-affine process with the scaling constant . The construction is extended to the multidimensional FBM field as well as to micropulses of more complicated shape.

Keywords: Fractal; sums; of; pulses; Fractal; sums; of; micropulses; Fractional; Brownian; motion; Poisson; random; measure; Self-similarity; Self-affinity; Stationarity; of; increments (search for similar items in EconPapers)
Date: 1995
References: View complete reference list from CitEc
Citations: View citations in EconPapers (19) Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(95)00046-1
Full text for ScienceDirect subscribers only

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:spapps:v:60:y:1995:i:1:p:1-18

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().

 
Page updated 2020-03-29
Handle: RePEc:eee:spapps:v:60:y:1995:i:1:p:1-18