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On the solution of Markov's parabolic equation for the second‐order spaced frequency and position coherence function
Author(s) -
Bitjukov A. A.,
Gherm V. E.,
Zernov N. N.
Publication year - 2002
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/2001rs002491
Subject(s) - quadratic equation , coherence (philosophical gambling strategy) , position (finance) , mathematics , markov chain , mathematical analysis , formalism (music) , representation (politics) , function (biology) , markov process , statistical physics , physics , geometry , art , musical , statistics , finance , evolutionary biology , politics , political science , law , economics , visual arts , biology
An analytic technique has been developed to construct the asymptotic representation of the spaced position and frequency coherence function in Markov's diffusive approximation. The technique employs the formalism of the quasi‐classic complex paths in an extended complex‐valued coordinate space. It allows the construction of the coherency for arbitrary realistic models of the structure function of the fluctuations of the refractive index of the medium of propagation. The technique has been employed to obtain explicit analytic asymptotic solutions for some realistic models of the structure function. For the quadratic structure function the method produces the known rigorous solution in an automatic fashion.