Real almost zeros of random polynomials with complex coefficients
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 form...
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| Published in: | International journal of stochastic analysis Vol. 2005; no. 2; pp. 195 - 209 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.01.2005
|
| ISSN: | 2090-3332, 2090-3340 |
| Online Access: | Get full text |
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| Summary: | 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
. |
|---|---|
| ISSN: | 2090-3332 2090-3340 |
| DOI: | 10.1155/JAMSA.2005.195 |