Non-reversible lifts of reversible diffusion processes and relaxation times

• 成果类型: Article; Early Access
• 署名作者: Eberle, Andreas; Loerler, Francis
• 署名单位: University of Bonn
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01308-x
• 发表日期: 2024
• 关键词: deterministic markov-processes; kinetic-equations; mcmc; hypocoercivity

摘要

We propose a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivity based on space-time Poincar & eacute; inequalities can be rephrased and simplified in the language of lifts and how it can be applied to find optimal lifts.