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Nguyen Dinh Cong

Publications and source records attributed to Nguyen Dinh Cong.

6 recordsLinked to original sources
arXiv2025

Stability criteria for rough systems

We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide stability criteria for a stationary solution of the continuous system to be exponentially stable, provided the diffusion term is bounded and its derivatives exhibit small growth. The same conclusions hold for the regular discretization scheme with a sufficiently small step size, but one needs to apply the sewing lemma and stopping times for the discrete time set. Our stability criteria are based on the linearization of the drift and require only information about the bound and growth rates of the diffusion, making them data-driven criteria.

math.DS↗
arXiv2020

Pullback attractors for stochastic Young differential delay equations

We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main results show that, if there is a linear part in the drift term which has no delay factor and has eigenvalues of negative real parts, then the generated random dynamical system possesses a random pullback attractor provided that the Lipschitz coefficients of the remaining parts are small.

math.DS↗
arXiv2019

Asymptotic stability for stochastic dissipative systems with a Hölder noise

We prove the exponential stability of the zero solution of a stochastic differential equation with a Hölder noise, under the strong dissipativity assumption. As a result, we also prove that there exists a random pullback attractor for a stochastic system under a multiplicative fractional Brownian noise.

math.PR↗
arXiv2019

Lyapunov spectrum of nonautonomous linear Young differential equations

We show that a linear Young differential equation generates a topological two-parameter flow, thus the notions of Lyapunov exponents and Lyapunov spectrum are well-defined. The spectrum can be computed using the discretized flow and is independent of the driving path for triangular systems which are regular in the sense of Lyapunov. In the stochastic setting, the system generates a stochastic two-parameter flow which satisfies the integrability condition, hence the Lyapunov exponents are random variables of finite moments. Finally, we prove a Millionshchikov theorem stating that almost all, in a sense of an invariant measure, linear nonautonomous Young differential equations are Lyapunov regular.

math.DS↗
arXiv2017

Nonautonomous Young differential equations revisited

In this paper we prove that under weak conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions. The proofs use estimates in p-variation norms, greedy time techniques, and Gronwall-type lemma with the help of Shauder theorem of fixed points.

math.PR↗