On the average number of sharp crossings of certain Gaussian random polynomials
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On the Average Number of Sharp Crossings of Certain Gaussian Random Polynomials
Let Qn(x) = ∑n i=0 Aix i be a random algebraic polynomial where the coefficients A0, A1, · · · form a sequence of centered Gaussian random variables. Moreover, assume that the increments ∆j = Aj−Aj−1, j = 0, 1, 2, · · · are independent, assuming A−1 = 0. The coefficients can be considered as n consecutive observations of a Brownian motion. We obtain the asymptotic behaviour of the expected numb...
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عنوان ژورنال
دوره 37 شماره No. 1
صفحات 81- 92
تاریخ انتشار 2011-06-01
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