Contents
Chapter 1. Introduction 1
Chapter 2. The Fundamental Solution of the Wave Equation and the
Covariance Function 7
2.1. Some Properties of the Fundamental Solution and Its Regularisations 7
2.2. The Covariance Function and Riesz Kernels 9
Chapter 3. older-Sobolev Regularity of the Stochastic Integral 13
3.1. Regularity in Space 14
3.2. Regularity in Time 26
Chapter 4. Path Properties of the Solution of the Stochastic Wave Equation 33
4.1. Existence, Uniqueness and Moments 33
4.2. Regularity in the Space Variable 37
4.3. Regularity in the Time Variable 43
Chapter 5. Sharpness of the Results 49
Chapter 6. Integrated Increments of the Covariance Function 53
6.1. Spatial Increments 53
6.2. Increments in Time 56
Bibliography 69
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