Wave Equation With A Coloured Stable Noise

We define a random measure generated by a real anisotropic harmonizable fractional stable field ZHZH with stability parameter α∈(1,2)α∈(1,2) and Hurst index H∈(12,1)H∈(12,1) and prove that the measure is σ-additive in probability. An integral with respect to this measure is constructed, which enables us to consider a wave equation in R3ℝ3 with a random source generated by ZHZH. We show that the solution to this equation, given by Kirchhoff’s formula, has a modification, which is Hölder continuous of any order up to (3H−1)∧1(3⁢H-1)∧1. In the case where H∈(23,1)H∈(23,1), we show further that the modification is absolutely continuous.