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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Fourier transform of general stochastic measures

V. M. Radchenko, N. O. Stefans'ka

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Abstract: The Fourier transform of general stochastic measures in is defined. The inversion theorem for this transform is proved, connection with convergence of stochastic integrals is established. Example of applying for convergence of solutions of stochastic heat equation is considered.

Keywords: Stochastic measure, Fourier transform of random processes, weak convergence, stochastic heat equation

Bibliography:
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2. V. Radchenko, Integrals w.r.t. general stochastic measure, Institute of Mathematics, Kyiv, 1999.
3. V. Radchenko, Riemann integral of a random function and the parabolic equation with a general stochastic measure, Theor. Prob. and Math. Stat. 87 (2012), 163–175.
4. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes, Chapman & Hall,Boca Raton, 1994.
5. I. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, “Mir”, Moscow,1974.
6. V. Radchenko, Mild solution of the heat equation with a general stochastic measure, Studia Mathematica 194 (2009), no, 3, 231-251.