On a class of martingale problems on Banach spaces
On a class of martingale problems on Banach spaces
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DOI：
10.1214/ejp.v18-2924
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发表时间：
2010-09
影响因子：
1.4
通讯作者：
M. Kunze
中科院分区：
文献类型：
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作者：
M. Kunze
我们引入了局部鞅问题的半线性随机发展方程驱动的圆柱维纳过程和建立一个一对一的对应关系的鞅问题的解决方案和（解析）弱解的随机方程。我们还证明了适定方程的解是强马尔可夫过程。我们将我们的结果应用到半线性随机方程的加性噪声的半线性项仅仅是可测的和随机反应扩散方程的Ho lder连续乘性噪声。
We introduce the local martingale problem associated to semilinear stochastic evolution equations driven by a cylindrical Wiener process and establish a one-to-one correspondence between solutions of the martingale problem and (analytically) weak solutions of the stochastic equation. We also prove that the solutions of well-posed equations are strong Markov processes. We apply our results to semilinear stochastic equations with additive noise where the semilinear term is merely measurable and to stochastic reaction-diffusion equations with Ho lder continuous multiplicative noise.