Search results for "Markov"
showing 10 items of 628 documents
Importance sampling for Lambda-coalescents in the infinitely many sites model
2011
We present and discuss new importance sampling schemes for the approximate computation of the sample probability of observed genetic types in the infinitely many sites model from population genetics. More specifically, we extend the 'classical framework', where genealogies are assumed to be governed by Kingman's coalescent, to the more general class of Lambda-coalescents and develop further Hobolth et. al.'s (2008) idea of deriving importance sampling schemes based on 'compressed genetrees'. The resulting schemes extend earlier work by Griffiths and Tavar\'e (1994), Stephens and Donnelly (2000), Birkner and Blath (2008) and Hobolth et. al. (2008). We conclude with a performance comparison o…
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
2012
In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information
2014
This paper is concerned with the problem of H"~ filtering for a class of two-dimensional Markovian jump linear systems described by the Fornasini-Marchesini local state-space model. The systems under consideration are subject to state-delays and deficient mode information in the Markov chain. The description of deficient mode information is comprehensive that simultaneously includes the exactly known, partially unknown and uncertain transition probabilities. By invoking the properties of the transition probability matrix, together with the convexification of uncertain domains, a new H"~ performance analysis criterion for the filtering error system is firstly derived. Then, via some matrix i…
Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information
2014
Published version of an article in the journal: Multidimensional Systems and Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1007/s11045-013-0276-x This paper is concerned with the problem of {Mathematical expression} model approximation for a class of two-dimensional (2-D) discrete-time Markovian jump linear systems with state-delays and imperfect mode information. The 2-D system is described by the well-known Fornasini-Marchesini local state-space model, and the imperfect mode information in the Markov chain simultaneously involves the exactly known, partially unknown and uncertain transition probabilities. By using the characteristics of the transition proba…
A Note on Locally ??-compact Spaces
1995
: The local version of the concept of ℰτ-compactness (where ℰ is a class of Hausdorff spaces and ℰ is a cardinal) introduced by the first author as a generalization of Her-rlich's concept of ℰ-compactness (and hence, also of Mrowka's E-compactness) is defined and the corresponding theory is initiated. An essential part of the theory is developed under the additional assumption that all spaces from ℰ are absolute extensors for spaces under consideration. The theory contains as a special case the classical theory of local compactness.
System times and channel availability analyses in multi-channel cognitive radio networks
2014
Channel accessibility by a secondary user (SU) in cognitive radio networks (CRNs) depends on the availability of the spectrum based on primary user and other SU activities. A new SU request may be blocked and an ongoing SU service may also be discarded if no sufficient spectrum is available. So far, little work has been done to analyze the reliability and availability aspects of CRNs from the perspective of the dependability theory. In this paper, we introduce the concept of availability for spectrum access in multi-channel CRNs, which is defined as the fraction of time that a CRN can allocate at least the minimum number of required channels for a new SU request. Through a proposed continuo…
A space on which diameter-type packing measure is not Borel regular
1999
We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.
Hausdorff measures, Hölder continuous maps and self-similar fractals
1993
Let f: A → ℝn be Hölder continuous with exponent α, 0 < α ≼ 1, where A ⊂ ℝm has finite m-dimensional Lebesgue measure. Then, as is easy to see and well-known, the s-dimensional Hausdorif measure HS(fA) is finite for s = m/α. Many fractal-type sets fA also have positive Hs measure. This is so for example if m = 1 and f is a natural parametrization of the Koch snow flake curve in ℝ2. Then s = log 4/log 3 and α = log 3/log 4. In this paper we study the question of what s-dimensional sets in can intersect some image fA in a set of positive Hs measure where A ⊂ ℝm and f: A → ℝn is (m/s)-Hölder continuous. In Theorem 3·3 we give a general density result for such Holder surfacesfA which implies…
Convergence of Markov Chains
2020
We consider a Markov chain X with invariant distribution π and investigate conditions under which the distribution of X n converges to π as n→∞. Essentially it is necessary and sufficient that the state space of the chain cannot be decomposed into subspaces that the chain does not leave, or that are visited by the chain periodically; e.g., only for odd n or only for even n.
Markov Chains and Electrical Networks
2020
There is a natural connection between electrical networks and so called reversible Markov chains. An example for such a chain is the symmetric graph random walk which, in each step, jumps to a randomly chosen graph neighbor at equal probability. This connection is studied here in some detail. As an application, we prove the statement that if such a graph random walk is recurrent, then it is recurrent also on each subgraph. (Although this statement is rather plausible, it is hard to show by different means.) In particular, the graph random walk on a percolation cluster of the planar integer lattice is recurrent.