کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5130066 | 1378656 | 2017 | 23 صفحه PDF | دانلود رایگان |
In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst index Hâ(14,12). Initial data are assumed to be constant. First, we prove that this equation has a unique solution (in the Skorohod sense) and obtain an exponential upper bound for the p-th moment the solution, for any pâ¥2. Condition H>14 turns out to be necessary for the existence of solution. Secondly, we show that this solution coincides with the one obtained by the authors in a recent publication, in which the solution is interpreted in the Itô sense. Finally, we prove that the solution of the equation in the Skorohod sense is weakly intermittent.
Journal: Stochastic Processes and their Applications - Volume 127, Issue 7, July 2017, Pages 2316-2338