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Theory of Probability and Mathematical Statistics



WAVE EQUATION WITH STABLE NOISE

L. I. PRYHARA, G. M. SHEVCHENKO

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Abstract: We study a three-dimensional wave equation with a source having symmetric -stable distribution. Two cases are considered: where the perturbation is a white noise and where it is a coloured noise. In both cases we show that a candidate solution to the equation, given by the Kirchho formula, is a generalized solution.

Keywords: стохастичне диференціальне рівняння в частинних похідних, хвильове рівняння, розклад Лепажа, симетрична альфа-стійка випадкова міра, узагальнений розвязок, дійсне анізотропне дробове стійке поле.

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