From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions

Details From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions

2005-03-09

arxiv.org/abs/math/0503182v1

Mathematics

Probability

36 pages

Scientific paper

Multifractional Brownian motion is an extension of the well-known fractional Brownian motion where the Holder regularity is allowed to vary along the paths. In this paper, two kind of multi-parameter extensions of mBm are studied: one is isotropic while the other is not. For each of these processes, a moving average representation, a harmonizable representation, and the covariance structure are given. The Holder regularity is then studied. In particular, the case of an irregular exponent function H is investigated. In this situation, the almost sure pointwise and local Holder exponents of the multi-parameter mBm are proved to be equal to the correspondent exponents of H. Eventually, a local asymptotic self-similarity property is proved. The limit process can be another process than fBm.

Affiliated with

Also associated with

No associations

Rating

From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-369725