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One approach is to investigate the absolute error in the self-normalized central limit theorem via Berry-Esseen bounds or Edgeworth expansions.. This has been done by many
We prove an almost sure limit theorem on the exact convergence rate of the maximum of standardized gaussian random walk increments.. On a conjecture of R´
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
Key words: Central limit theorem, excited random walk, law of large numbers, positive and negative cookies, recurrence, renewal structure, transience.. AMS 2000 Subject
In particular, we prove a strong approximation result for such a random walk which, in turn, enables us to establish strong limit theorems, like the joint Strassen type law of
Abstract. Following the investigation by U. Thorbjørnsen, we present a simple differential approach to the limit theorems for empirical spectral distributions of complex random
Taking advantage of this decompo- sition we apply a theorem of Barbour and Xia [ 1 ] on translated compound Poisson approximation in total variation distance to the distributions
To prove this theorem we extend the bounds proved in [ 2 ] for the continuous time simple random walk on (Γ , µ ) to the slightly more general random walks X and Y defined
