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On exit laws for semigroups in weak duality

Imed Bachar (2001)

Commentationes Mathematicae Universitatis Carolinae

Let : = ( P t ) t > 0 be a measurable semigroup and m a σ -finite positive measure on a Lusin space X . An m -exit law for is a family ( f t ) t > 0 of nonnegative measurable functions on X which are finite m -a.e. and satisfy for each s , t > 0 P s ...

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

Mohamed Hmissi, Ezzedine 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 harmonic functions of symmetric Lévy processes

Ante Mimica (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in (Potential Anal.17 (2002) 375–388)) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Hölder continuity estimates of harmonic functions. Despite the failure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from (Probab. Theory Related Fields135 (2006) 547–575) and obtain asymptotic...

On homogenization of space-time dependent and degenerate random flows II

Rémi Rhodes (2008)

Annales de l'I.H.P. Probabilités et statistiques

We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle is proved for the critical rescaling of the diffusion. Here, we generalize this approach to diffusions whose space-time scaling differs from the critical one.

On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Ivo Punčochář, Miroslav Šimandl (2014)

International Journal of Applied Mathematics and Computer Science

The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that...

On iterates of strong Feller operators on ordered phase spaces

Wojciech Bartoszek (2004)

Colloquium Mathematicae

Let (X,d) be a metric space where all closed balls are compact, with a fixed σ-finite Borel measure μ. Assume further that X is endowed with a linear order ⪯. Given a Markov (regular) operator P: L¹(μ) → L¹(μ) we discuss the asymptotic behaviour of the iterates Pⁿ. The paper deals with operators P which are Feller and such that the μ-absolutely continuous parts of the transition probabilities P ( x , · ) x X are continuous with respect to x. Under some concentration assumptions on the asymptotic transition probabilities...

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