Using approximation technique, we introduce the concepts of canonical extension and symmetrio integral for jump process and obtain some results in the chaotic form.
In ref. [1] it is shown that the Mobius-Rota inversion can be generalized to any locallystandard infinite poset S in the nonstandard sense. The result is as follows. Let C be a locally<sup>*</sup>-finite p...In ref. [1] it is shown that the Mobius-Rota inversion can be generalized to any locallystandard infinite poset S in the nonstandard sense. The result is as follows. Let C be a locally<sup>*</sup>-finite poset with a 0-element O. Suppose that <sup>*</sup>μ<sub>1</sub>∈<sup>*</sup>I（C,<sup>*</sup>K）. a <sup>*</sup>-incidence algebra of C,over a field <sup>*</sup>K of characteristic O. possesses an inverse <sup>*</sup>μ<sub>2</sub>=<sup>*</sup>μ<sub>1</sub><sup>-1</sup>,where <sup>*</sup>μ<sub>1</sub>, <sup>*</sup>μ<sub>2</sub> are<sup>*</sup>-Mobius operators. Then for <sup>*</sup>f, <sup>*</sup>g∈Map （C. <sup>*</sup>K）, the functions from C into <sup>*</sup>K,展开更多
基金Supported in part by National Natural Science Foundation of China.
文摘Using approximation technique, we introduce the concepts of canonical extension and symmetrio integral for jump process and obtain some results in the chaotic form.
文摘In ref. [1] it is shown that the Mobius-Rota inversion can be generalized to any locallystandard infinite poset S in the nonstandard sense. The result is as follows. Let C be a locally<sup>*</sup>-finite poset with a 0-element O. Suppose that <sup>*</sup>μ<sub>1</sub>∈<sup>*</sup>I（C,<sup>*</sup>K）. a <sup>*</sup>-incidence algebra of C,over a field <sup>*</sup>K of characteristic O. possesses an inverse <sup>*</sup>μ<sub>2</sub>=<sup>*</sup>μ<sub>1</sub><sup>-1</sup>,where <sup>*</sup>μ<sub>1</sub>, <sup>*</sup>μ<sub>2</sub> are<sup>*</sup>-Mobius operators. Then for <sup>*</sup>f, <sup>*</sup>g∈Map （C. <sup>*</sup>K）, the functions from C into <sup>*</sup>K,
