On limit processes for a class of additive functional of recurrent diffusion processes
On limit processes for a class of additive functional of recurrent diffusion processes
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关于一类循环扩散过程的加性泛函的极限过程
DOI：
10.1007/bf00534253
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发表时间：
1979
期刊：
影响因子：
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通讯作者：
S. Kotani
中科院分区：
文献类型：
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作者：
Y. Kasahara;S. Kotani
关于一类可加泛函的极限定理，特别是Markov过程的占据时，已有许多作者研究过，如Darling-Kac [1]，Dobrushin [2]，Karlin-McGregor [-6]，C.石[-12]和笠原[7，8]。到目前为止，除[-12]外，这些定理只讨论了在每个固定时刻的收敛性，但最近Papanicolaou-Stroock-Varadhan [，10]讨论了作为随机过程的收敛性：例如，如果B（t）是一个一维布朗t运动，l（t，x）是它的局部时间（即，对于每个Borel，2 S l（t，x）dx=~ 1 E（B（s））ds
Limit theorems for a class of additive functionals, especially occupation times of Markov process, have been studied by many authors, eg, Darling-Kac [1], Dobrushin [2], Karlin-McGregor [-6], C. Stone [-12] and Kasahara [7, 8]. So far, these theorems except [-12] dealt with the convergence at each fixed time only, but recently Papanicolaou-Stroock-Varadhan [, 10] discussed the convergence as stochastic processes: for example, if b (t) is a 1-dimensional Brownian t motion and l (t, x) is its local time (ie, 2 S l (t, x) dx=~ 1E (b (s)) ds for every Borel