1987/04/01 by Donald W. K. Andrews, Andrews, Donald K. · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #Applied mathematics #Autoregressive model #Autoregressive moving average #Economic modeling #Economic models #Economic theory #Estimators #Independent and identically distributed random variables #Insurance, Mortality, Demography, Risk Management #Integrable system #Law of large numbers #Martingale (probability theory) #Martingales #Mathematical analysis #Mathematics #Mixing (physics) #Moment (physics) #Physics #Probability and Risk Models #Quantum mechanics #Random variable #Random variables #Statistical physics #Statistics #Stochastic processes and financial applications #Theoretical econometrics #Zero
paper · open access · doi:10.7907/3gv6t-s2w13
published in CaltechAUTHORS (California Institute of Technology) (California Institute of Technology)
openalex publication_date 1987/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
This paper provides L` and weak laws of large numbers for uniformly integrable L1-mixingales. The L1-mixingale condition is a condition of asymptotic weak temporal dependence that is weaker than most conditions considered in the literature. Processes covered by the laws of large numbers include martingale difference, Φ(.), ρ(.) and α(•) mixing, autoregressive moving average, infinite order moving average, near epoch dependent, L1-near epoch dependent, and mixingale sequences and triangular arrays. The random variables need not possess more than one moment finite and the L1-mixingale numbers need not decay to zero at any particular rate. The proof of the results is remarkably simple and completely self-contained.