The first exit of almost strongly recurrent semi-Markov processes

Joachim Domsta; Franciszek Grabski

Displaying similar documents to “The first exit of almost strongly recurrent semi-Markov processes”

A coupling technique for stochastic comparison of functions of Markov processes.

Doisy, M. (2000)

Journal of Applied Mathematics and Decision Sciences

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A note on bisexual Galton-Watson branching processes with immigration.

M. González, M. Molina, M. Mota (2001)

Extracta Mathematicae

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About stability of risk-seeking optimal stopping

Raúl Montes-de-Oca, Elena Zaitseva (2014)

Kybernetika

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We offer the quantitative estimation of stability of risk-sensitive cost optimization in the problem of optimal stopping of Markov chain on a Borel space $X$ . It is supposed that the transition probability $p (\cdot | x)$ , $x \in X$ is approximated by the transition probability $\tilde{p} (\cdot | x)$ , $x \in X$ , and that the stopping rule ${\tilde{f}}_{*}$ , which is optimal for the process with the transition probability $\tilde{p}$ is applied to the process with the transition probability $p$ . We give an upper bound (expressed in term of the total variation distance:...

Robust mixing.

Ganapathy, Murali (2007)

Electronic Journal of Probability [electronic only]

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On the core property of the cylinder functions class in the construction of interacting particle systems

Anja Voss-Böhme (2011)

Kybernetika

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For general interacting particle systems in the sense of Liggett, it is proven that the class of cylinder functions forms a core for the associated Markov generator. It is argued that this result cannot be concluded by straightforwardly generalizing the standard proof technique that is applied when constructing interacting particle systems from their Markov pregenerators.

Monte Carlo simulation of Markov chain steady-state distribution.

Abdelaziz Nasroallah (2004)

Extracta Mathematicae

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A note on the diffusive scaling limit for a class of linear systems.

Nagahata, Yukio, Yoshida, Nobuo (2010)

Electronic Communications in Probability [electronic only]

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Strangely sweeping one-dimensional diffusion

Ryszard Rudnicki (1993)

Annales Polonici Mathematici

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Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = ProbX(t) ≥ 0 as t → ∞ and construct an equation such that $l i m s u p_{t \to \infty} t^{- 1} \int_{0}^{t} p (s) d s = 1$ and $l i m i n f_{t \to \infty} t^{- 1} \int_{0}^{t} p (s) d s = 0$ .

Inessentiality with respect to subspaces

Michael Levin (1995)

Fundamenta Mathematicae

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Let X be a compactum and let $A = (A_{i}, B_{i}) : i = 1, 2, . . .$ be a countable family of pairs of disjoint subsets of X. Then A is said to be essential on Y ⊂ X if for every closed $F_{i}$ separating $A_{i}$ and $B_{i}$ the intersection $(\cap F_{i}) \cap Y$ is not empty. So A is inessential on Y if there exist closed $F_{i}$ separating $A_{i}$ and $B_{i}$ such that $\cap F_{i}$ does not intersect Y. Properties of inessentiality are studied and applied to prove: Theorem. For every countable family of pairs of disjoint open subsets of a compactum X there exists an open set G ∩ X on...

A problem of Galambos on Engel expansions

Jun Wu (2000)

Acta Arithmetica

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1. Introduction. Given x in (0,1], let x = [d₁(x),d₂(x),...] denote the Engel expansion of x, that is, (1) $x = 1 / d ₁ (x) + 1 / (d ₁ (x) d ₂ (x)) + . . . + 1 / (d ₁ (x) d ₂ (x) . . . d_{n} (x)) + . . .$ , where $d_{j} (x), j \geq 1$ is a sequence of positive integers satisfying d₁(x) ≥ 2 and $d_{j + 1} (x) \geq d_{j} (x)$ for j ≥ 1. (See [3].) In [3], János Galambos proved that for almost all x ∈ (0,1], (2) $l i m_{n \to \infty} d_{n}^{1 / n} (x) = e .$ He conjectured ([3], P132) that the Hausdorff dimension of the set where (2) fails is one. In this paper, we prove this conjecture: Theorem. $d i m_{H} x \in (0, 1] : (2) f a i l s = 1$ . We use L¹ to denote the one-dimensional Lebesgue measure on (0,1] and $d i m_{H}$ to denote...

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

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Let $F_{i} = 1, . . ., N$ be affine mappings of $ℝ^{n}$ . It is well known that if there exists j ≤ 1 such that for every $σ_{1}, . . ., σ_{j} \in 1, . . ., N$ the composition (1) $F_{σ 1} \circ . . . \circ F_{σ_{j}}$ is a contraction, then for any infinite sequence $σ_{1}, σ_{2}, . . . \in 1, . . ., N$ and any $z \in ℝ^{n}$ , the sequence (2) $F_{σ 1} \circ . . . \circ F_{σ_{n}} (z)$ is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any $z \in ℝ^{n}$ and any $σ = σ_{1}, σ_{2}, . . .$ belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every $σ = σ_{1}, σ_{2}, . . . \in Σ$ the composition (1) is a contraction....