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Mathematical Analysis of Random Noise-Conclusion
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This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.read more
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A detailed statistical representation of the local structure of optical vortices in random wavefields
TL;DR: In this article, the statistical properties near phase singularities in a complex wavefield are studied by means of the conditional distributions of the real and imaginary Gaussian components, given a common zero crossing point.
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Real zeros of random algebraic polynomials with binomial elements
Kambiz Farahmand,Ahmad Nezakati +1 more
TL;DR: In this paper, the authors provided an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial, where the number of zeros is defined as the sum of the real number of zero points of the polynomials.
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Large Mean out Crossing of Nonlinear Response to Stochastic Input
TL;DR: In this article, the mean out-crossing rate of a nonlinear system subjected to stochastic excitation is computed by use of the first-order reliability method, FORM.
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Algebraic polynomials with random coefficients with binomial and geometric progressions.
Kambiz Farahmand,M. Sambandham +1 more
TL;DR: In this paper, the expected number of real zeros of an algebraic polynomial ao+a1x+a2x2+⋯+anxn with random coefficient aj,j=0,1,2,n is known.
Journal ArticleDOI
Outcrossings of safe regions by generalized hyperbolic processes
TL;DR: In this paper, a simple Gaussian mixture model with generalized hyperbolic marginals is presented, starting with Rice's celebrated formula for level upcrossings and outcrossings of safe regions.