MARTINGALE CENTRAL LIMIT THEOREM AND NONUNIFORMLY HYPERBOLIC SYSTEMS A Dissertation Presented by LUKE MOHR Approved as to style and content by: Hongkun Zhang, Chair Luc Rey-Bellet, Member Bruce Turkington, Member Jonathan Machta Physics, Outside Member Michael Lavine, Department Head Mathematics and Statistics.
In most cases the multiple (random) fields of martingale differences is given by a completely commuting filtration. A central limit theorem proving convergence to a normal law has been known for Bernoulli random fields and in (V15) this result was extended to random fields where one of generating transformations is ergodic. In the present paper.
Summary This chapter contains sections titled: Preliminaries and Motivation Convergence of Martingale Difference Arrays Weak Convergence of the Process, U(n) Bibliographic Notes A Martingale Central Limit Theorem - 2005 - Wiley Series in Probability and Statistics - Wiley Online Library.
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Abstract. A theorem on the weak convergence of a properly normalized multivariate continuous local martingale is proved. The time-change theorem used for this purpose allows for short and transparent arguments. 1991 Mathematics Subject Classification: 60F05, 60G44 Keywords and Phrases: Continuous martingales, weak convergence, time-change device, nested filtrations, stable convergence.
Theorem 1 contains a type of martingale characteristic function convergence which is strictly analogous to the classical CLT, while Theorem 2 provides weak convergence of finite dimensional distributions to those of a Wiener process, followed by (Theorem 3) the weak convergence of corresponding induced measures on C (0, 1) to Wiener measure, thus entailing an invariance principle for.
A Martingale Central Limit Theorem Sunder Sethuraman We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given. Lemma 1. For n 1, let U n;T n be random variables such that 1. U n!ain probability. 2. fT ngis uniformly integrable. 3. fjT nU njgis uniformly integrable. 4. E(T n) !1. Then E(T nU n) !a. Proof. Write T.
A Nonuniform Bound on the Rate of Convergence in the Martingale Central Limit Theorem Haeusler, Erich and Joos, Konrad, Annals of Probability, 1988; A note on exact convergence rates in some martingale central limit theorems Renz, Joachim, Annals of Probability, 1996; Law of large numbers for critical first-passage percolation on the triangular lattice Yao, Chang-Long, Electronic.