Dalang R.C. Hölder-Sobolev regularity of the solution to the stochastic wave equation in dimension three / R.C.Dalang, M.Sanz-Solé. - Providence: American Mathematical Society, 2009. - vi, 70 p. - (Memoirs of the American Mathematical Society; Vol.199, N 931). - Bibliogr.: p.69-70. - ISBN 978-0-8218-4288-1; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / 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. Holder-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