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| Dirichlet Forms and Symmetric Diffusions on a Bounded Domain in R^d |
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Citation： |
Yan Jiaan,Zhang Tusheng.Dirichlet Forms and Symmetric Diffusions on a Bounded Domain in R^d[J].Chinese Annals of Mathematics B,1990,11(4):418~425 |
| Page view： 795
Net amount： 974 |
Authors： |
Yan Jiaan; Zhang Tusheng |
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| Abstract： |
Let D be a bounded C^3-domain in R^d and (a_ij) be a bounded symmetric matrix defined on D. Consider the symmetric form
$\[\varepsilon u,v) = \frac{1}{2}\sum\limits_{i,j = 1}^d {\int_D {{a_{ij}}(x)\frac{{\partial u(x)}}{{\partial {x_i}}}\frac{{\partial v(x)}}{{\partial {x_j}}}dx,u,v \in {H^1}(D)} } \]$
Under some assumptions it is shown that the diffusion process associated with the regular Dirichlet space (\varepsilon,(H^1(D)) on L^2(\bar D) can be characterized as a unique solution of a certain stochastic differential equation. |
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