Abstract
We considered a method for the determining of the statistical characteristics of the magnitude, location and first-passage time of Markov random process, with piecewise constant drift and diffusion coefficients. We found the closed analytical expressions for distribution functions of the specified random variables. We also analyzed the asymptotic behavior of probability density and ordinary moments of location of the greatest maximum of Markov random process and showed their coincidence with some known results for the particular cases.
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