Memoirs of the American Mathematical Society 2009; 70 pp; softcover Volume: 199 ISBN10: 0821842889 ISBN13: 9780821842881 List Price: US$60 Individual Members: US$36 Institutional Members: US$48 Order Code: MEMO/199/931
 The authors study the sample path regularity of the solution of a stochastic wave equation in spatial dimension \(d=3\). The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. The authors prove that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any fixed \(x\in\mathbb{R}^3\), the sample paths in time are Hölder continuous functions. Further, the authors obtain joint Hölder continuity in the time and space variables. Their results rely on a detailed analysis of properties of the stochastic integral used in the rigourous formulation of the s.p.d.e., as introduced by Dalang and Mueller (2003). Sharp results on one and twodimensional space and time increments of generalized Riesz potentials are a crucial ingredient in the analysis of the problem. For spatial covariances given by Riesz kernels, the authors show that the Hölder exponents that they obtain are optimal. Table of Contents  Introduction
 The fundamental solution of the wave equation and the covariance function
 HölderSobolev regularity of the stochastic integral
 Path properties of the solution of the stochastic wave equation
 Sharpness of the results
 Integrated increments of the covariance function
 Bibliography
