Stefanska N. Fourier transform of general stochastic measures and its application

Representations of stochastic processes by random series is an important tool for the approximation of random functions. Representations of stochastic processes in the form of random series are studied starting from the well-known Paley – Wiener decomposition for the Wiener process. Wavelet decompositions of stochastic processes have been studied recently. There is an extensive literature devoted to Fourier series with random coefficients and their sums. Stochastic processes and random series generated by a general stochastic measure defined on Borel subsets of and are considered in this thesis. The only restriction imposed on the measure is the -additivity in probability. We do not impose any restriction on like nonnegativity or existence of moments. Such the function is called the general stochastic measure. By analogy with the classical case, we introduce the Fourier series and Fourier – Haar series for general stochastic measures. We prove that the values of µ as well as the values of stochastic integrals with respect to can be approximated with the help of these series.