Strong mixing Markov semigroups on C₁ are meager

Wojciech Bartoszek; Beata Kuna

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Displaying similar documents to “Strong mixing Markov semigroups on C₁ are meager”

Markov's property of the Cantor ternary set

Leokadia Białas, Alexander Volberg (1993)

Studia Mathematica

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We prove that the Cantor ternary set E satisfies the classical Markov inequality (see [Ma]): for each polynomial p of degree at most n (n = 0, 1, 2,...) (M) $| p^{'} (x) | \leq M n^{m} s u p_{E} | p |$ for x ∈ E, where M and m are positive constants depending only on E.

Mean lower bounds for Markov operators

Eduard Emel&#039;yanov, Manfred Wolff (2004)

Annales Polonici Mathematici

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Let T be a Markov operator on an L¹-space. We study conditions under which T is mean ergodic and satisfies dim Fix(T) < ∞. Among other things we prove that the sequence $(n^{- 1} \sum_{k = 0}^{n - 1} T^{k}) ₙ$ converges strongly to a rank-one projection if and only if there exists a function 0 ≠ h ∈ L¹₊ which satisfies $l i m_{n \to \infty} | | (h - n^{- 1} \sum_{k = 0}^{n - 1} T^{k} f) ₊ | | = 0$ for every density f. Analogous results for strongly continuous semigroups are given.

Tangential Markov inequality in $L^{p}$ norms

Agnieszka Kowalska (2015)

Banach Center Publications

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In 1889 A. Markov proved that for every polynomial p in one variable the inequality $| | p^{'} {| |}_{[- 1, 1]} {\leq (d e g p) ² | | p | |}_{[- 1, 1]}$ is true. Moreover, the exponent 2 in this inequality is the best possible one. A tangential Markov inequality is a generalization of the Markov inequality to tangential derivatives of certain sets in higher-dimensional Euclidean spaces. We give some motivational examples of sets that admit the tangential Markov inequality with the sharp exponent. The main theorems show that the results on certain arcs...

Compact subsets of $C^{n}$ preserving Markov’s inequality

W. Plesniak (1988)

Matematički Vesnik

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A note on Markov operators and transition systems

Bartosz Frej (2002)

Colloquium Mathematicae

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On a compact metric space X one defines a transition system to be a lower semicontinuous map $X \to 2^{X}$ . It is known that every Markov operator on C(X) induces a transition system on X and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated. ...

The Nagaev-Guivarc’h method via the Keller-Liverani theorem

Loïc Hervé, Françoise Pène (2010)

Bulletin de la Société Mathématique de France

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The Nagaev-Guivarc’h method, via the perturbation operator theorem of Keller and Liverani, has been exploited in recent papers to establish limit theorems for unbounded functionals of strongly ergodic Markov chains. The main difficulty of this approach is to prove Taylor expansions for the dominating eigenvalue of the Fourier kernels. The paper outlines this method and extends it by stating a multidimensional local limit theorem, a one-dimensional Berry-Esseen theorem, a first-order...

Semiflows and semigroups

Edoardo Vesentini (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Given a compact Hausdorff space $K$ and a strongly continuous semigroup $T$ of linear isometries of the Banach space of all complex-valued, continuous functions on $K$ , the semiflow induced by $T$ on $K$ is investigated. In the particular case in which $K$ is a compact, connected, differentiable manifold, a class of semigroups $T$ preserving the differentiable structure of $K$ is characterized.

An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games

Kristal K. Trejo, Julio B. Clempner, Alexander S. Poznyak (2016)

Kybernetika

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This paper presents a novel approach for computing the strong Stackelberg/Nash equilibrium for Markov chains games. For solving the cooperative $n$ -leaders and $m$ -followers Markov game we consider the minimization of the $L_{p} -$ norm that reduces the distance to the utopian point in the Euclidian space. Then, we reduce the optimization problem to find a Pareto optimal solution. We employ a bi-level programming method implemented by the extraproximal optimization approach for computing the strong...

Kantorovich-Rubinstein Maximum Principle in the Stability Theory of Markov Semigroups

Henryk Gacki (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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A new sufficient condition for the asymptotic stability of a locally Lipschitzian Markov semigroup acting on the space of signed measures $_{s i g}$ is proved. This criterion is applied to the semigroup of Markov operators generated by a Poisson driven stochastic differential equation.

Polynomial inequalities on general subsets of $R^{N}$

Pierre Goetgheluck (1989)

Colloquium Mathematicae

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Compactness properties of Feller semigroups

G. Metafune, D. Pallara, M. Wacker (2002)

Studia Mathematica

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We study the compactness of Feller semigroups generated by second order elliptic partial differential operators with unbounded coefficients in spaces of continuous functions in $ℝ^{N}$ .

Eigenvalues of operators in $L_{p}$ -spaces in Markov chains with a general state space

Zbyněk Šidák (1967)

Czechoslovak Mathematical Journal

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Sets with the Bernstein and generalized Markov properties

Mirosław Baran, Agnieszka Kowalska (2014)

Annales Polonici Mathematici

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It is known that for $C^{\infty}$ determining sets Markov’s property is equivalent to Bernstein’s property. We are interested in finding a generalization of this fact for sets which are not $C^{\infty}$ determining. In this paper we give examples of sets which are not $C^{\infty}$ determining, but have the Bernstein and generalized Markov properties.

The scaling limits of a heavy tailed Markov renewal process

Julien Sohier (2013)

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

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In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the $α$ -stable regenerative set. We then apply these results to the strip wetting model which is a random walk $S$ constrained above a wall and rewarded or penalized when it hits the strip $[0, \infty) \times [0, a]$ where $a$ is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.