Some results about multifactor uncertain differential equations with
applications to extreme values and time integral
Abstract
Previous literature has proved that there exists a unique solution about
multifactor uncertain differential equation (MUDE for short) when their
coefficients satisfy strict global Lipschitz continuous condition. In
this paper, firstly, we consider new existence and uniqueness theorem
under the weaker local Lipschitz continuous condition. The next, when
the coefficients do not satisfy the Lipschitz condition, we just
showcase existence theorem under continuous and linear growth
conditions. Once more, we establish the inverse uncertainty
distributions (IUDs for short) of supremum, infimum and time integral
about the uncertain process Zk, meanwhile, we design some numerical
algorithms for solving these IUDs. In the end, some numerical examples
are presented to verify the effectiveness of algorithms.