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Real almost zeros of random polynomials with complex coefficients

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  • K. Farahmand
  • A. Grigorash
  • P. Flood

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 .

Suggested Citation

  • K. Farahmand & A. Grigorash & P. Flood, 2005. "Real almost zeros of random polynomials with complex coefficients," International Journal of Stochastic Analysis, Hindawi, vol. 2005, pages 1-15, January.
    • Handle: RePEc:hin:jnijsa:281505
    DOI: 10.1155/JAMSA.2005.195
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