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There are also some extra difficulties; for example we need to establish results related to the Cental Limit Theorem which are standard for random walks but apparently not
Key words: Brownian sheet, functional central limit theorem, Hölder space, invariance princi- ple, triangular array, summation process.. AMS 2000 Subject Classification:
The purpose of this note is to prove a central limit theorem for the third integrated moment of the Brownian local time increments using techniques of stochastic analysis.. This
Recently, the central limit theorem for product of sums has also been studied for dependent random variables (c.f., Gonchigdanzan and Rempala (2006)).. In this note, we will show
In Section 6 we prove Theorem 3.2 about the convergence of the renormalization branching process to a time-homogeneous limit.. In Section 7 , we prove the statements from
In this note, we study the Gaussian fluctuations of the edge occupation measure for a reversible Markov chain and give a nice description of the covariance matrix.. Then we give
Furthermore, Kesten and Zhang (1997) showed a central limit theorem for the passage time in the undirected critical model.. Here, we partially verify (1.14) for the directed
But by the central limit theorem for m-dependent stationary sequence (see for example Brockwell and Davis, 1990, page 213), the latter is asymptotically normal with mean zero
