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On exit laws for subordinated semigroups by means of 𝒞 1 -subordinators

Mohamed HmissiEzzedine Mliki — 2010

Commentationes Mathematicae Universitatis Carolinae

We study the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of bounded operators acting on L 2 ( m ) . We mainly investigate subordinated semigroups in the Bochner sense by means of 𝒞 1 -subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup.

On gradient-like random dynamical systems

Aya HmissiFarida HmissiMohamed Hmissi — 2012

ESAIM: Proceedings

This paper deals with some characterizations of gradient-like continuous random dynamical systems (RDS). More precisely, we establish an equivalence with the existence of random continuous section or with the existence of continuous and strict Liapunov function. However and contrary to the deterministic case, parallelizable RDS appear as a particular case of gradient-like RDS. The obtained results are generalizations of well-known analogous theorems in the framework of deterministic...

On the helix equation

Mohamed HmissiImene Ben SalahHajer Taouil — 2012

ESAIM: Proceedings

This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝ d , (t, ω) ↦ H(t, ω) of the helix equation H ( 0 ) = 0 ; H ( s + t,ω ) = H ( s, Φ ( t,ω ) ) + H ( t,ω ) where Φ : ℝ × Ω → Ω, (t, ω) ↦ Φ(t, ω) is a dynamical system...

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