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A Property of Two-Parameter Generalized Transition Function

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Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

We find that a generalized transition function P s,t (x, y, z,A) with two parameters s, t > 0 on a measurable space has a very interesting and important property: its total transition probability P s,t (x, y, z, E) is only related to the product st of the two parameters s, t > 0 and is unrelated to the states x, y, z ∈ E. To be more exact, there is a constant 0 ≤ λ ≤ + ∞ such that

P s,t (x, y, z, E) ≡ exp(-λst), ∀s, t > 0, x, y, z ∈ E.

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Author information

Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, P.R. China, 411105

    Yuquan Xie

Authors
  1. Yuquan Xie
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Xie, Y. (2011). A Property of Two-Parameter Generalized Transition Function. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_36

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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