Initial measures for the stochastic heat equation

Daniel Conus, Mathew Joseph, Davar Khoshnevisan, Shang Yuan Shiu

研究成果: 雜誌貢獻期刊論文同行評審

14 引文 斯高帕斯(Scopus)

摘要

We consider a family of nonlinear stochastic heat equations of the form ∂tu = Lu + σ(u)W, where W denotes space- time white noise, L the generator of a symmetric Lévy process on R, and σ is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure u0. Tight a priori bounds on the moments of the solution are also obtained. In the particular case that Lf = cf'' for some c > 0, we prove that if u0 is a finite measure of compact support, then the solution is with probability one a bounded function for all times t > 0.

原文???core.languages.en_GB???
頁(從 - 到)136-153
頁數18
期刊Annales de l'institut Henri Poincare (B) Probability and Statistics
50
發行號1
DOIs
出版狀態已出版 - 2月 2014

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