Unbiased Time-Average Estimators for Markov Chains

• 成果类型: Article
• 署名作者: Kahale, Nabil
• 署名单位: heSam Universite; ESCP Business School
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0326
• 发表日期: 2024
• 页码: 2136-2165
• 关键词: monte-carlo methods; simulation; EFFICIENCY

摘要

We consider a time-average estimator fk of a functional of a Markov chain. Under a coupling assumption, we show that the expectation of f(k) has a limit mu as the number of time steps goes to infinity. We describe a modification of f(k) that yields an unbiased estimator f(k) of mu. It is shown that f(k) is square integrable and has finite expected running time. Under certain conditions, f(k) can be built without any precomputations and is asymptotically at least as efficient as f(k), up to a multiplicative constant arbitrarily close to one. Our approach also provides an unbiased estimator for the bias of f(k). We study applications to volatility forecasting, queues, and the simulation of high-dimensional Gaussian vectors. Our numerical experiments are consistent with our theoretical findings.