Probability transformation method for the evaluation of derivative, integral and Fourier transform of some stochastic processes

Autor: Giovanni Falsone, Rossella Laudani
Rok vydání: 2021
Předmět:
Zdroj: Journal of Engineering Mathematics. 131
ISSN: 1573-2703
0022-0833
DOI: 10.1007/s10665-021-10183-7
Popis: This work shows as the use of the Probability Transformation Method (PTM) allows producing some numerical approaches able to evaluate the probability density functions (PDFs) of the derivative, the integral and the Fourier transform of a given process, in which PDF is known. The probabilistic characterization through the knowledge of the PDF is very useful, above all for non-Gaussian processes that should be approximately defined by high-order moments, or cumulants, etc. It is evidenced that the process defined by the derivative of another one requires the knowledge of the last process at two close instants, while, for the integral process evaluation at a fixed time, it is necessary to know the probabilistic characterization of the integrand process from the initial time. The procedure for the integral processes has been applied for defining a numerical approach for the evaluation of the Fourier transform of a given approach. The applications of these procedures to some simple examples, compared with Monte Carlo simulation results, have evidenced good properties in both the accuracy and computational effort.
Databáze: OpenAIRE
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