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Stability and Synchronization Control of Stochastic Neural Networks pp 1–11Cite as

Relative Mathematic Foundation

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 35))

Abstract

In this chapter, we will present some concepts and formulas as well as several important inequalities which will be used throughout this book. We will begin with some elementary concepts and formulas, such as stochastic processes and martingales, SDEs, M-matrix, and Itô’s formula. Then some inequalities frequently used in this book will follow in the sequel.

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Author information

Authors and Affiliations

  1. School of Information Sciences and Technology, Donghua University, Shanghai, China

    Wuneng Zhou & Liuwei Zhou

  2. Anyang Normal University, Anyang, China

    Jun Yang

  3. Shanghai University of Engineering Science, Shanghai, China

    Dongbing Tong

Authors
  1. Wuneng Zhou
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  2. Jun Yang
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  3. Liuwei Zhou
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  4. Dongbing Tong
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Corresponding author

Correspondence to Wuneng Zhou .

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Zhou, W., Yang, J., Zhou, L., Tong, D. (2016). Relative Mathematic Foundation. In: Stability and Synchronization Control of Stochastic Neural Networks. Studies in Systems, Decision and Control, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47833-2_1

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  • DOI: https://doi.org/10.1007/978-3-662-47833-2_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47832-5

  • Online ISBN: 978-3-662-47833-2

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