再论两参数Wiener过程的增量有多小
Theorizing Again about How Small Are the Increments of the Two-parameter Wiener Processes
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摘要: 本文将对两参数Wiener过程的增量有多小的问题作更进一步的讨论。我们将找出正则化因子μT 使得\liminf _T \rightarrow \infty \mu_T \inf _0 \leq y \leq T-a_T \inf _0 \leq x \leq 1-h_T \sup _0 \leq t \leq a_T \sup _0 \leq s \leq h_T|W(R)|,的下极限为1;我们还将找出正则化因子vT,使得\limsup _T \rightarrow \infty \nu_T \inf _0 \leq y \leq T-a_T \inf _0 \leq x \leq 1-h_T \sup _0 \leq t \leq a_T \sup _0 \leq s \leq h_T|W(R)|的上极限为1。Abstract: ln this paper we discuss how small are the increments of the two-parameter Wiener processes. We find norrnaling factor μT such that \liminf _T \rightarrow \infty \mu_T \inf _0 \leq y \leq T-a_T \inf _0 \leq x \leq 1-h_T \sup _0 \leq t \leq a_T \sup _0 \leq s \leq h_T|W(R)|=1, and normalizing factor vT such that \limsup _T \rightarrow \infty \nu_T \inf _0 \leq y \leq T-a_T \inf _0 \leq x \leq 1-h_T \sup _0 \leq t \leq a_T \sup _0 \leq s \leq h_T|W(R)|=1
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