A class of spatio-temporal and causal stochastic processes, with application to multiscaling and multifractality
Date
2005
Journal Title
Journal ISSN
Volume Title
Publisher
Academy of Science for South Africa
Abstract
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Lévy type whose weighted amplitudes are integrated within a causality cone. General n-point correlations are derived in closed form. As a special case of the general framework, we consider a causal multiscaling process in space and time in more detail. The latter is derived from, and completely specifed by, power-law two-point correlations, and gives rise to scaling behaviour of both purely temporal and spatial higher-order correlations. We further establish the connection to classical multifractality and prove the multifractal nature of the coarse-grained field amplitude.
Description
CITATION: Schmiegel, S., Barndorff-Nielsen, O. E. & Eggers, H. C. 2005. A class of spatio-temporal and causal stochastic processes, with application to multiscaling and multifractality. South African Journal of Science, 101(11-12):513-519.
The original publication is available at https://journals.co.za
The original publication is available at https://journals.co.za
Keywords
Fractals, Stochastic processes
Citation
Schmiegel, S., Barndorff-Nielsen, O. E. & Eggers, H. C. 2005. A class of spatio-temporal and causal stochastic processes, with application to multiscaling and multifractality. South African Journal of Science, 101(11-12):513-519