2 6 Ju l 2 00 5 Weak Convergence of the Scaled Median of Independent Brownian Motions ∗
نویسنده
چکیده
We consider the median of n independent Brownian motions, denoted byMn(t), and show that √ nMn converges weakly to a centered Gaussian process. The chief difficulty is establishing tightness, which is proved through direct estimates on the increments of the median process. An explicit formula is given for the covariance function of the limit process. The limit process is also shown to be Hölder continuous with exponent γ for all γ < 1/4.
منابع مشابه
A ug 2 00 6 Weak Convergence of the Scaled Median of Independent Brownian Motions ∗
We consider the median of n independent Brownian motions, denoted byMn(t), and show that √ nMn converges weakly to a centered Gaussian process. The chief difficulty is establishing tightness, which is proved through direct estimates on the increments of the median process. An explicit formula is given for the covariance function of the limit process. The limit process is also shown to be Hölder...
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تاریخ انتشار 2007