2012/11/23 by Geoffrey Decrouez, Owen Dafydd Jones · 5 citations
Mathematics · Physics and Astronomy · #Branching (polymer chemistry) #Branching process #Cascade #Class (philosophy) #Markov chain #Markov process #Mathematical Dynamics and Fractals #Multifractal system #Representation (politics) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR
paper · pdf · doi:10.1214/11-aap834
published in The Annals of Applied Probability 22(6) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/11-AAP834 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2012/11/23 · arxiv created 2012/11/28 · arxiv updated 2012/11/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a new class of multifractal process on ℝ, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the boundaries of multitype Galton–Watson trees. Our class of processes includes Brownian motion subjected to a continuous multifractal time-change. In addition, if we observe our process at a fixed spatial resolution, then we can obtain a finite Markov representation of it, which we can use for on-line simulation. That is, given only the Markov representation at step n, we can generate step n+1 in O(log n) operations. Detailed pseudo-code for this algorithm is provided.