JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (6): 23-31.doi: 10.6040/j.issn.1671-9352.0.2019.655

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Bochner-Wick integral for S *(M)space

SHI Jia, WANG Cai-shi, ZHANG Li-xia, ZHANG Yin   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-06-01

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Abstract: Let S *(M)be a generalized functional space of discrete-time normal martingale M. This paper introduces and discusses the integral operation of S *(M)-valued measure and S *(M)-valued function in the framework of Bernoulli noise analysis. First of all, the concept of S *(M)-valued measure is defined. On this basis, this paper deeply investigates the properties of S *(M)-valued measure by Fock transform, and obtains the appropriate conditions for the countably additive of this kind of measure in the sense of norm. Next, Bochner-Wick integral for S *(M)-valued function with respect to S *(M)-valued measure is defined and the corresponding control convergence theorem is established.

Key words: discrete-time normal martingale, Fock transform, Bochner-Wick integral, vector measure

CLC Number: 

  • O211.63
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