Abstract
Uncertain differential equation is a type of differential equation involving uncertain process. This paper will give uncertainty distributions of the extreme values, first hitting time, and integral of the solution of uncertain differential equation. Some solution methods are also documented in this paper.
Highlights
Probability theory, since it was founded by Kolmogorov in 1933, has been a crucial tool to model indeterminacy phenomena when probability distributions of the possible events are available
We study the extreme values of the solution of an uncertain differential equation, and give their uncertainty distributions in the section of Extreme values
Extreme values we study the extreme values of the solution of an uncertain differential equation, and give their uncertainty distributions
Summary
Probability theory, since it was founded by Kolmogorov in 1933, has been a crucial tool to model indeterminacy phenomena when probability distributions of the possible events are available. (Liu and Ha [31]) Let ξ1, ξ2, · · · , ξn be independent uncertain variables with uncertainty distributions 1, 2, · · · , n, respectively. (Yao and Chen [17]) Let Xt and Xtα be the solution and α-path of the uncertain differential equation dXt = f (t, Xt)dt + g(t, Xt)dCt, respectively. Let Xt be the solution of an uncertain differential equation dXt = f (t, Xt)dt + g(t, Xt)dCt. Assume Xt has an uncertainty distribution t(x) at each time t.
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