Local Hölder regularity for set-indexed processes

Details Local Hölder regularity for set-indexed processes Local Hölder regularity for set-indexed processes

2012-03-04

arxiv.org/abs/1203.0750v1

Mathematics

Probability

39 pages, 2 figures

Scientific paper

In this paper, we study the H\"older regularity of set-indexed stochastic processes defined in the framework of Ivanoff-Merzbach. The first key result is a H\"older-continuity Theorem derived from the approximation of the indexing collection by a nested sequence of finite subcollections. H\"older-continuity based on the increment definition for set-indexed processes is also considered. Then, the localization of these properties leads to various definitions of H\"older exponents. Moreover, a pointwise continuity exponent is defined in relation with the weak continuity property for set-indexed processes which only considers single point jumps. In the case of Gaussian processes, almost sure values are proved for the H\"older exponents. As an application, the local regularity of the set-indexed fractional Brownian motion and the Ornstein-Uhlenbeck process are proved to be constant, with probability one.

Affiliated with

Also associated with

No associations

Rating

Local Hölder regularity for set-indexed processes 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 Local Hölder regularity for set-indexed processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local Hölder regularity for set-indexed processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-332360