2004/03/03 by Taoufik Bouziane, Bouziane, Taoufik
Computer Science · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Probability (math.PR) #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #math.MG #math.PR
paper · pdf · doi:10.48550/arxiv.math/0403080
20 pages
openalex publication_date 2004/03/03 · arxiv created 2004/11/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this work is to construct a \it Brownian motion with values in simplicial complexes with piecewise differential structure. In order to state and prove the existence of such Brownian motion, we define a family of continuous Markov processes with values in an admissible complex; we call every process of this family, \it isotropic transport process. We show that the family of the isotropic processes contains a subsequence, which converges weakly to a measure; we name it the \it Wiener measure. Then, using the finite dimensional distributions of the obtained Wiener measure, we construct a new admissible complex valued continuous Markov process: the Brownian motion. We finished with a geometric analysis of this Brownian motion, to determine the recurrent or transient behavior of such process.