Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 2, Pages 195-209
doi:10.1155/JAMSA.2005.195
Real almost zeros of random polynomials with complex coefficients
School of Computing and Mathematics, Faculty of Engineering, University of Ulster at Jordanstown, Co. Antrim, BT37 0QB, UK
Received 30 April 2004; Revised 14 July 2004
Copyright © 2005 K. Farahmand et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We present a simple formula for the expected number
of times that a complex-valued Gaussian stochastic process has a
zero imaginary part and the absolute value of its real part is
bounded by a constant value
M. We show that only some mild
conditions on the stochastic process are needed for our formula to
remain valid. We further apply this formula to a random algebraic
polynomial with complex coefficients. We show how the above
expected value in the case of random algebraic polynomials varies
for different behaviour of
M.