PROBABILITY DISTRIBUTION OF CROSS-FUNCTIONAL FROM REGULAR SIGNAL AND NORMAL MARKOVIAN NOISE

Abstract

A superposition of a regular function ts )( and a random process tx )( with the properties of normality and Markov property is considered. For a given time interval, based on the specified function, the convolutiontype functional is studied. An approach based on the use of reverse functions is proposed and used, which made it possible to obtain an analytical expression for the generating distribution function of random values of the convolution functional. The statistical properties of the convolution functional are analyzed. The density and the integral distribution law are found numerically using the inverse Laplace transform for the selected regular function ts )( and the selected values T of the observation time, the decrement of the random process ν and its intensity 2 σ X . It is shown that an increase in the parameter 2 Tσ X leads to the expansion of the convolution functional to the peripheral regions of large deviations. A decrease in the parameter νT leads to the localization of the values of the convolution functional in the fluctuation region. The probability distribution density of the convolution functional has a single maximum, two inflection points and exponential asymptotic behavior at the periphery.