STOCHASTIC PDEs WITH FUNCTION-VALUED SOLUTIONS ∗)
STOCHASTIC PDEs WITH FUNCTION-VALUED SOLUTIONS ∗)
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具有函数值解的随机偏微分方程 *)
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
M. Curie
中科院分区：
文献类型：
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作者：
A. Karczewska;J. Zabczyk;M. Curie
本文给出了Rd上随机热波动方程有函数值解的充要条件。结果扩展到所有维度d和所有空间均匀扰动，最近的特征由大朗和Frangos（DaFr）。本文提出了一个自然的框架，研究非线性随机方程。它是以函数空间中的调和分析技术和随机积分理论为基础的。推广到d维环面和非线性方程进行了讨论。
The paper provides necessary and sufficient conditions underwhich stochas- tic heat and wave equations on R d have function-valued solutions. The results extend, to all dimensions d and to all spatially homogeneous perturbations, recent characterizations by Dalang and Frangos (DaFr). The paper proposes a natural framework for a study of nonlinear stochastic equations. It is based on the har- monic analysis technique and on the stochastic integration theory in functional spaces. Generalizations to the d-dimensional torus and to nonlinear equations are discussed as well.