Stochastic Limit Theory : An Introduction for Econometricians

By S. Gregoir. 1996

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Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning (2019, methodology): “In addition, from the definition of α–mixing and its moment inequality, for any bounded function f(x) with mean with respect to the stationary distribution, based on (Davidson, 1994, Theorem 14.2), we know ‖P[f(st, at, st+1, rt) | s0, a0, s1, r0]‖1 ≤ 2(21/2 + 1)αt‖f(st, at, st+1, rt)‖∞.”
Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model (2004, background): “This is the condition that there exists a locally measurable (finite-lag) approximation to u t , which is a uniform mixing process, given that e t is independent (e.g. Davidson 1994 Theorem 14.1).”
Local Projection Inference Is Simpler and More Robust Than You Think (2020, background): “But this is a well-known result from the unit root literature (e.g., Hamilton, 1994, Chapter 17.4), since {ut} satisfies a Functional Central Limit Theorem under Assumptions 1 and 2 (Davidson, 1994, Theorem 27.14).”