Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 2, Pages 195-209
doi:10.1155/JAMSA.2005.195
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.