Lyapunov-type conditions and stochastic differential equations driven by $G$-Brownian motion
Xinpeng Li, Xiangyun Lin, Yiqing Lin
TL;DR
This paper investigates the existence, uniqueness, and stability of stochastic differential equations driven by G-Brownian motion, using Lyapunov-type conditions and localization methods to establish core theoretical results.
Contribution
It provides new Lyapunov-type criteria for stability and proves existence and uniqueness of solutions for locally Lipschitz GSDEs under G-Brownian motion.
Findings
Existence and uniqueness of solutions for locally Lipschitz GSDEs
Lyapunov-type conditions ensure stability of GSDEs
Localization methods are effective for solving GSDEs
Abstract
This paper studies the solvability and the stability of stochastic differential equations driven by G-Brownian motion (GSDEs). In particular, the existence and uniqueness of the solution for locally Lipschitz GSDEs is obtained by localization methods, also the stability of such GSDEs are discussed with Lyapunov-type conditions.
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Taxonomy
TopicsStochastic processes and financial applications · Stability and Controllability of Differential Equations · Nonlinear Differential Equations Analysis