Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Opuscula Mathematica

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On potential kernels associated with random dynamical systems

Hmissi M., Mokchaha F., Hmissi A.

Opuscula Mathematica

2015

Vol. 35, no. 4

499--515

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.

On the Bochner subordination of exit laws

Hmissi M., Maaouia W.

Opuscula Mathematica

2011

Vol. 31, no. 2

195-207

Let P = (Pt)t≥0 be a sub-Markovian semigroup on L2(m), let β = (βt)t≥0 be a Bochner subordinator and let Pβ = (Pβ(t ))t≥0 be the subordinated semigroup of P by means of β, i.e. Pβ(s):= ∫∞(0) Pr βs(dr). Let φ:= (φt)t>0 be a P-exit law, i.e. Ptφs = φs+t, s,t>0 and let φβ(t):= ∫∞(0)φs βt(ds). Then φβ:= (φβ(t)t>0 is a Pβ-exit law whenever it lies in L2(m). This paper is devoted to the converse problem when β is without drift. We prove that a Pβ-exit law ψ:= (ψt)t>0 is subordinated to a (unique) P-exit law φ (i.e. ψ= φ β) if and only if (Ptu)t>0 ⊂ D(Aβ), where u = ∫∞(0)e-s ψ sds and Aβ, is the L2(m)-generator of Pβ.