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|Title: ||On the Rate of Moment Convergence for a Normalized Random Walk|
|Authors: ||Cheng, Tsung-Lin;Chow, Yuan-Shih;Yan, Yung-Lu|
|Keywords: ||Convergence of moment;Edgeworth expansion;Random walk|
|Issue Date: ||2012-09-10T06:02:37Z
|Abstract: ||In this paper, we study the convergence rate of the r-th moments of a normalized|
simple random walk. When r = 1, we use the discrete-time version of Ito-Tanaka formula
to obtain an exact convergence rate. Since there is no corresponding Ito-Tanaka
formula for general r > 0, we adopt the Edgeworth expansion to derive bounds for the
rates of convergence. Finally, we carry out some simulations to illustrate the convergence
and, as a byproduct, propose an alternative way, among others, to approximate
the value of π.
|Relation: ||Journal of the Chinese Statistical Association, 49(1): 1-25|
|Appears in Collections:||[數學系] 期刊論文|
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