Functional SPDE with Multiplicative Noise and Dini Drift
Functional SPDE with Multiplicative Noise and Dini Drift
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DOI：
10.5802/afst.1544
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发表时间：
2015-05
期刊：
影响因子：
--
通讯作者：
X. Huang;F.-Y. Wang
中科院分区：
文献类型：
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作者：
X. Huang;F.-Y. Wang
证明了一类带乘性噪声和Dini连续漂移的半线性泛函SPDEs温和解的存在唯一性和非爆炸性。在有限维有界时滞情形下，得到了log-Harnack不等式和$L^2$-梯度估计.由于马尔可夫半群与方程的泛函（段）解相联系，需要对时滞时间区间内解的路径空间进行分析。
Existence, uniqueness and non-explosion of the mild solution are proved for a class of semi-linear functional SPDEs with multiplicative noise and Dini continuous drifts. In the finite-dimensional and bounded time delay setting, the log-Harnack inequality and $L^2$-gradient estimate are derived. As the Markov semigroup is associated to the functional (segment) solution of the equation, one needs to make analysis on the path space of the solution in the time interval of delay.