Martingale Limit Theory and Its ApplicationInequalities and laws of large numbers; The central limit theorem; Invariance principles in the central limit theorem and law of the iterated logarithm; Limit theory for stationary processes via corresponding results for approximating martingales; Estimation of parameters from stochastic processes; Miscellaneous applications. |
Contents
3 | 52 |
5 | 71 |
Invariance Principles in the Central Limit Theorem and | 97 |
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a.s. limit analog application assumption Brownian motion central limit theorem Chapter completes the proof constant converges a.s. converges in distribution converges in probability Corollary deduce defined denote dlog ergodic sequence ergodic theorem example finite follows function Furthermore Hannan hence Heyde holds Ibragimov implies independent r.v. inequality invariance principle iterated logarithm Kronecker's lemma large numbers least squares Lemma lim inf lim sup limit results log log martingale martingale convergence theorem martingale differences martingale limit Math ML estimator nonnegative norming o-field obtain parameter probability space proof of Theorem prove random variables rate of convergence S₁ satisfied stationary ergodic stationary process stochastic processes strong law subadditive subadditive process submartingale sufficient sums of independent Suppose t₁ term Theorem 5.2 theory uniformly integrable variance X₁ Y₁ zero zero-mean Σ Σ σ²