Work

A Functional Central Limit Theorem for the General Brownian Motion on the Half-Line

Year: 2024

Type: preprint

Abstract: In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative estimates in the vague topology at any fixed time. As important applications, we deduce functional central limit theorems for random walks on the positive integers with boundary conditions, which converge to Brownian motions on the positive half-line with boundary conditions at zero.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2408.06830

Authors: Erhard, Dirk, Franco, Tertuliano, Jara, Milton, Pimenta, Eduardo

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa do Estado da Bahia, Instituto Serrapilheira

Awards: G1244575561, G3023667051, G3081379008, G7053727760

OpenAlex ID: W4402427191

Cites:

Cited by:

Related to: 10