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Uncertain calculus with renewal process

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Abstract

Uncertain calculus is a branch of mathematics that deals with differentiation and integration of function of uncertain processes. As a fundamental concept, uncertain integral has been defined with respect to canonical process. However, emergencies such as economic crisis and war occur occasionally, which may cause the uncertain process a sudden change. So far, uncertain renewal process has been employed to model these jumps. This paper will present a new uncertain integral with respect to renewal process. Besides, this paper will propose a type of uncertain differential equation driven by both canonical process and renewal process.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Kai Yao

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  1. Kai Yao
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Correspondence to Kai Yao.

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Yao, K. Uncertain calculus with renewal process. Fuzzy Optim Decis Making 11, 285–297 (2012). https://doi.org/10.1007/s10700-012-9132-y

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  • DOI: https://doi.org/10.1007/s10700-012-9132-y

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