Uncertain calculus with renewal process
- 377 Downloads
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.
KeywordsUncertain calculus Uncertain integral Renewal process Uncertain differential equation Uncertainty theory
Unable to display preview. Download preview PDF.
- Chen X. (2011) American option pricing formula for uncertain financial market. International Journal of Operations Research 8(2): 32–37Google Scholar
- Ito K. (1944) Stochastic integral. Proceedings of the Japan Academy, Tokyo, Japan, pp 519–524Google Scholar
- Liu B. (2008) Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems 2(1): 3–16Google Scholar
- Liu B. (2009b) Some research problems in uncertainty theory. Journal of Uncertain Systems 3(1): 3–10Google Scholar
- Liu B. (2010a) Uncertainty theory: A branch of mathematics for modeling human uncertainty. Springer, BerlinGoogle Scholar
- Liu B. (2010b) Uncertain set theory and uncertain inference rule with application to uncertain control. Journal of Uncertain Systems 4(2): 83–98Google Scholar
- Liu B. (2010c) Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems 4(3): 163–170Google Scholar
- Liu B. (2011) Uncertain logic for modeling human language. Journal of Uncertain Systems 5(1): 3–20Google Scholar
- Peng J., Yao K. (2010) A new option pricing model for stocks in uncertainty markets. International Journal of Operations Research 7(4): 213–224Google Scholar
- Wang X., Gao Z., Guo H. (2012) Delphi method for estimating uncertainty distributions. Information: An International Interdisciplinary Journal 15(2): 449–460Google Scholar
- Wiener N. (1923) Differential space. Journal of Mathematical Physics 2: 131–174Google Scholar