Algebraic polynomials with random coefficients

K. Farahmand

International Journal of Stochastic Analysis, 2002, vol. 15, 1-6

Abstract:

This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a 0 ( ω ) + a 1 ( ω ) ( n 1 ) 1 / 2 x + a 2 ( ω ) ( n 2 ) 1 / 2 x 2 + … a n ( ω ) ( n n ) 1 / 2 x n when n is large. The coefficients { a j ( w ) } j = 0 n , w ∈ Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space ( A , Ω , Pr ) . A special case of dependent coefficients is also studied.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:463458

DOI: 10.1155/S1048953302000084

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