关于一个特殊的Markov过程

On a Special Markov process

设G是R^d(d≥2)中的一个有界C^1区域,则(1/2D,H^1(G))是一个具有局部性质的正则Dirichlet形式。本文中我们研究与(1/2D,H^1(G))相对应的对称Warkov过程{X_t}。在第一节中我们证明了X_t满足广义Tanaka公式;在第二节中我们利用X_t解决了区域G上一类Schf(?)dinger方程的Neumann问题。

Let G be a bounded (?)1 domain of Rd (d≥2) . Then(1/2|D,H1 ( G)) is a regular Dirichlet form.In this paper we studied the symmetric Markov process Xt corresponding to (1/2|D, H1 (G)).In Section 1 we proved that the process Xt satisfies the generalized Tanaka' s formula; in Section 2 we solved the Neumann problem on the domain G of a class of Schrodinger equations by using the process Xt.