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THE DISTRIBUTION DENSITY OF SQUARE VALUE PROBABILITIES FUNCTIONALITY FROM TRAJECTORIES OF WIENER PROCESS

Natalia N. Vitokhina, Yuriy P. Virchenko, Natalya A. Zinchenko, Natalya N. Mot’kina, Vladimir A. Esin, Anna N

Abstract


In the article authors develop an approach to calculating the statistic development probability for composite functions of square values in Gaussian casual process trajectories. Calculating distribution density for additive composite functions is based on standard Wiener process trajectories. Authors have developed a density formula for uniformly convergent decomposition, with x = 0. The convergence is exponentially fast. The calculation of the approximated probability is presented:


Keywords


stationary processes; casual Gaussian processes; Wiener process; the density of distribution of probabilities; additive functionality; return transformation of Laplace; calculating the successive approximations; accuracy assessment

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References


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DOI: http://dx.doi.org/10.6084/ijact.v8i6.949

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