Stability in p -th moment for multifactor uncertain differential equation

Abstract

Uncertain differential equation plays an important role in dealing with dynamical systems with uncertainty. The uncertain factor of influencing dynamical system is not alone in many situations. Multifactor uncertain differential equation is a type of differential equation driven by multiple Liu processes. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper focuses on the stability in p-th moment for multifactor uncertain differential equation, including the concept of stability in p-th moment, and the sufficient condition for multifactor uncertain differential equation being stable in p-th moment. The relationship between stability in p-th moment and stability in measure is also discussed. Moreover, applications in finance and population dynamics are documented.

Parameter estimation in multifactor uncertain population model

“…Zhang [20] focused on the stability in measure and the stability in mean of multifactor uncertain differential equation. Ma [21] discussed the concept of stability in p -th moment for multifactor uncertain differential equation and documents its application. Sheng [22] presented a concept of the almost sure stability of multifactor uncertain differential equation.…”

Parameter estimation in multifactor uncertain population model

“…Zhang [20] focused on the stability in measure and the stability in mean of multifactor uncertain differential equation. Ma [21] discussed the concept of stability in p -th moment for multifactor uncertain differential equation and documents its application. Sheng [22] presented a concept of the almost sure stability of multifactor uncertain differential equation.…”

New sufficient conditions for p-th moment stability of uncertain delay differential equation

“…Recent years, researches on stability in p -th moment for uncertain system are emerging one after another. For example, stability in p -th moment for multifactor UDE [20], UDE with jumps [21], multi-dimensional UDE [22], uncertain heat equations [23] and uncertain spring vibration equation [24] were successively investigated.…”

Parameter estimation in multifactor uncertain population model

“…Zhang [20] focused on the stability in measure and the stability in mean of multifactor uncertain differential equation. Ma [21] discussed the concept of stability in p -th moment for multifactor uncertain differential equation and documents its application. Sheng [22] presented a concept of the almost sure stability of multifactor uncertain differential equation.…”

New sufficient conditions for p-th moment stability of uncertain delay differential equation

“…Recent years, researches on stability in p -th moment for uncertain system are emerging one after another. For example, stability in p -th moment for multifactor UDE [20], UDE with jumps [21], multi-dimensional UDE [22], uncertain heat equations [23] and uncertain spring vibration equation [24] were successively investigated.…”

Parameter estimation in multifactor uncertain population model

“…Zhang [20] focused on the stability in measure and the stability in mean of multifactor uncertain differential equation. Ma [21] discussed the concept of stability in p -th moment for multifactor uncertain differential equation and documents its application. Sheng [22] presented a concept of the almost sure stability of multifactor uncertain differential equation.…”

New sufficient conditions for p-th moment stability of uncertain delay differential equation

“…Recent years, researches on stability in p -th moment for uncertain system are emerging one after another. For example, stability in p -th moment for multifactor UDE [20], UDE with jumps [21], multi-dimensional UDE [22], uncertain heat equations [23] and uncertain spring vibration equation [24] were successively investigated.…”