On potential kernels associated with random dynamical systems

• Autorzy: Hmissi M. , Mokchaha F. , Hmissi A.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.4.499

• Języki publikacji: EN

Abstrakty

EN

Let (Θ, φ) be a continuous random dynamical system defined on a probability space (Ω, F, P) and taking values on a locally compact Hausdorff space E. The associated potential kernel V is given by [formula]. In this paper, we prove the equivalence of the following statements: 1. The potential kernel of (Θ, φ) is proper, i.e. V ƒ is x-continuous for each bounded, x-continuous function with uniformly random compact support. 2. (Θ, φ) has a global Lyapunov function, i.e. a function L : Ω x E → (0, ∞) which is x-continuous and L,(Θ tω, φ(t, ω)x) ↓0 as t ↑ ∞. In particular, we provide a constructive method for global Lyapunov functions for gradient-like random dynamical systems. This result generalizes an analogous theorem known for deterministic dynamical systems.

Słowa kluczowe

EN

dynamical system; random dynamical systems; random differential equations; stochastic differential equation; potential kernel; domination principle; Lyapunov function

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 4
• Strony: 499--515
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Hmissi M.

• Universite de Tunis Elmanar Faculte des Sciences de Tunis Departement de Mathematiques TN-2092 Elmanar, Tunis, Tunisia
• Al-Imam Muhammad Ibn Saud Islamic University College of Science Department of Mathematics and Statistics P.O. Box 90950, Riyadh 11623, Saudi Arabia

autor

Mokchaha F.

• Universite de Tunis Elmanar Faculte des Sciences de Tunis Departement de Mathematiques TN-2092 Elmanar, Tunis, Tunisia
• Al-Imam Muhammad Ibn Saud Islamic University College of Science Department of Mathematics and Statistics P.O. Box 90950, Riyadh 11623, Saudi Arabia

autor

Hmissi A.

• Universite de Tunis Elmanar Faculte des Sciences de Tunis Departement de Mathematiques TN-2092 Elmanar, Tunis, Tunisia

Bibliografia

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