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Characteristic Function of the Markov Random Flight in Higher Dimensions [Articol]
(2024) Kolesnik, Alexander D.
Two series representations of the characteristic function of the multidimensional symmetric Markov random flight, are presented. These series are the decompositions of the characteristic function with respect to Bessel functions and with respect to time variable, whose coefficients are given by recurrent relations, as well as in the form of special determinants. Basing on these series representations, an asymptotic formula for the second moment function of the process, is obtained.
Some Analytical Properties of the Laplace Transform of the Characteristic Function of the Three-Dimensional Markov Random [Articol]
(2024) Kolesnik, Alexander D.
The analytical properties of the Laplace transform of the characteristic function of the three-dimensional symmetric Markov random flight, are studied. The only singular point (ordinary pole) and the residue at this point are evaluated, which gives the first coefficient (by the negative power of complex variable) in the Laurent decomposition of the Laplace-Fourier transform of the transition density of the process.