Infinite-dimensional stochastic differential equations related to Bessel random point fields

2014/05/02 by Ryuich Honda, Honda, Ryuich, Hirofumi Osada +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #15A52 #60J60 #60K35 #82B21 #82C22 #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1405.0523

openalex publication_date 2014/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve the infinite-dimensional stochastic differential equations (ISDEs) describing an infinite number of Brownian particles in ℝ⁺ interacting through the two-dimensional Coulomb potential. The equilibrium states of the associated unlabeled stochastic dynamics are Bessel random point fields. To solve these ISDEs, we calculate the logarithmic derivatives, and we prove that the random point fields are quasi-Gibbsian.

Cited by

• Infinite Interacting Brownian Motions and EVI Gradient Flows

Related

• Infinite-dimensional stochastic differential equations related to random\n matrices
• Infinite-Dimensional Stochastic Differential Equations and Diffusion Dynamics of Coulomb Random Point Fields
• Infinite-dimensional stochastic differential equations and tail σ-fields
• Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials II: Airy random point field
• Dynamical rigidity of stochastic Coulomb systems in infinite-dimensions