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On Expected Number of Level Crossings of a Random Hyperbolic Polynomial
| Content Provider | Semantic Scholar |
|---|---|
| Author | Sahoo, L. N. |
| Copyright Year | 2015 |
| Abstract | Let g1(ω), g2(ω), . . . , gn(ω) be independent and normally distributed random variables with mean zero and variance one. We show that, for large values of n, the expected number of times the random hyperbolic polynomial y = g1(ω) coshx + g2(ω) cosh 2x + · · · + gn(ω) coshnx crosses the line y = L, where L is a real number, is 1 π logn+ O(1) if L = o( √ n) or L/ √ n = O(1), but decreases steadily as O(L) increases in magnitude and ultimately becomes negligible when n−1 logL/ √ n → ∞. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://rmmc.eas.asu.edu/rmj/rmjVOLS2/vol45/vol45-4/maha.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Polynomial Sample Variance |
| Content Type | Text |
| Resource Type | Article |
