Construction of the Paths of Brownian Motions on Star Graphs

2011/02/22 by Vadim Kostrykin, Kostrykin, Vadim, Jürgen Potthoff +3 · 3 citations
Economics, Econometrics and Finance · Mathematics · #05C99 #35K05 #58J65 #60H99 #60J45 #60J65 #Brownian motion #Combinatorics #Computer science #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical economics #Mathematics #Probability (math.PR) #Star (game theory) #Statistics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:05C99 #msc:35K05 #msc:58J65 #msc:60H99 #msc:60J45 #msc:60J65

paper · pdf · doi:10.48550/arxiv.1102.4533

published in arXiv (Cornell University) (Cornell University) · 36 pages. The material of our previous articles 1012.0733, 1012.0737, 1012.0739 has been re-organized. The present article is a self contained version of 1012.0737

arxiv created 2011/02/22 · openalex publication_date 2011/02/22 · arxiv updated 2011/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of star graphs are given.

Citations

• A Note on Feller Semigroups and Resolvents
• Lower Limit for the Energy Derivative of the Scattering Phase Shift
• The Parabolic Differential Equations and the Associated Semi-Groups of Transformations

Cited by

• Brownian Motions on Metric Graphs with Non-Local Boundary Conditions I: Characterization
• Brownian Motions on Star Graphs with Non-Local Boundary Conditions

Related

• Brownian Motions on Metric Graphs II - Construction of Brownian Motions on Single Vertex Graphs
• Brownian Motions on Star Graphs with Non-Local Boundary Conditions
• Brownian Motions on Metric Graphs with Non-Local Boundary Conditions II: Construction
• Brownian Motions on Metric Graphs III - Construction: General Metric Graphs
• Brownian Motions on Metric Graphs with Non-Local Boundary Conditions I: Characterization