On exponential stability for stochastic differential equations disturbed by G-Brownian motion

2013/11/28 by Weiyin Fei, Fei, Weiyin, Chen Fei +1 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.PR #msc:60H10

paper · pdf · doi:10.48550/arxiv.1311.7311

arXiv admin note: text overlap with arXiv:1002.4546 by other authors

arxiv created 2013/11/28 · arxiv updated 2013/12/02

Abstract

We first introduce the calculus of Peng's G-Brownian motion on a sublinear expectation space (Ω, \cal H, 𝔼). Then we investigate the exponential stability of paths for a class of stochastic differential equations disturbed by a G-Brownian motion in the sense of quasi surely (q.s.). The analyses consist in G-Lyapunov function and some special inequalities. Various sufficient conditions are obtained to ensure the stability of strong solutions. In particular, by means of our results we generalize the one in the classical stochastic differential equations. Finally, an illustrative example is given.

Citations

• Nonlinear Expectations and Stochastic Calculus under Uncertainty

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