2018/03/19 by Florian Werner, Werner, Florian
Economics, Econometrics and Finance · Mathematics · #05C99 #35K05 #58J65 #60H99 #60J45 #60J65 #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1803.07027
openalex publication_date 2018/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Brownian motions on star graphs in the sense of Itô-McKean, that is, Walsh processes admitting a generalized boundary behavior including stickiness and jumps and having an angular distribution with finite support, are examined. Their generators are identified as Laplace operators on the graph subject to non-local Feller-Wentzell boundary conditions. A pathwise description is achieved for every admissible boundary condition: For finite jump measures, a construction of Kostrykin, Potthoff and Schrader in the continuous setting is expanded via a technique of successive killings and revivals; for infinite jump measures, the pathwise solution of Itô-McKean for the half line is analyzed and extended to the star graph. These processes can then be used as main building blocks for Brownian motions on general metric graphs with non-local boundary conditions.