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

Ryuich Honda; Hirofumi Osada

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

Probability 2015-05-12 v2

Authors: Ryuich Honda , Hirofumi Osada

Abstract

We solve the infinite-dimensional stochastic differential equations (ISDEs) describing an infinite number of Brownian particles in $\mathbb{R}^+$ 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.

Keywords

stochastic differential equations partial differential equations gaussian random fields

Cite

@article{arxiv.1405.0523,
  title  = {Infinite-dimensional stochastic differential equations related to Bessel random point fields},
  author = {Ryuich Honda and Hirofumi Osada},
  journal= {arXiv preprint arXiv:1405.0523},
  year   = {2015}
}

Comments

Accepted in Stochastic Processes and Their Applications. 29 pages

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