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Alternative Markov Properties for Chain Graphs
Scandinavian Journal of Statistics, 2001Graphical Markov models use graphs to represent possible dependences among statistical variables. Lauritzen, Wermuth, and Frydenberg (LWF) introduced a Markov property for chain graphs (CG): graphs that can be used to represent both structural and associative dependences simultaneously and that include both undirected graphs (UG) and acyclic directed ...
Andersson, Steen A. +2 more
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Topologically Recurrent Markov Chains: Ergodic Properties
Theory of Probability & Its Applications, 1987See the review in Zbl 0623.60088.
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Independence properties of directed markov fields
Networks, 1990AbstractWe investigate directed Markov fields over finite graphs without positivity assumptions on the densities involved. A criterion for conditional independence of two groups of variables given a third is given and named as the directed, global Markov property. We give a simple proof of the fact that the directed, local Markov property and directed,
Lauritzen, S. L. +3 more
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Convergence Properties of Perturbed Markov Chains
Journal of Applied Probability, 1998In this paper, we consider the question of which convergence properties of Markov chains are preserved under small perturbations. Properties considered include geometric ergodicity and rates of convergence. Perturbations considered include roundoff error from computer simulation.
Roberts, G. O. +2 more
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2015
In the previous chapter, we have considered SDEs where the integral is with respect to a general semimartingale. In this chapter, we focus our attention on a much more specialized setting, where the integral is taken with respect to time (i.e. Lebesgue measure), a Brownian motion and a compensated Poisson random measure.
Samuel N. Cohen, Robert J. Elliott
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In the previous chapter, we have considered SDEs where the integral is with respect to a general semimartingale. In this chapter, we focus our attention on a much more specialized setting, where the integral is taken with respect to time (i.e. Lebesgue measure), a Brownian motion and a compensated Poisson random measure.
Samuel N. Cohen, Robert J. Elliott
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1976
During all of our discussion of Markov chains, we shall wish to confine ourselves to stochastic processes defined on a sequence space. We have shown that an arbitrary stochastic process may be considered as a process on a suitable Ω in which the outcome functions f n are coordinate functions.
John G. Kemeny +2 more
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During all of our discussion of Markov chains, we shall wish to confine ourselves to stochastic processes defined on a sequence space. We have shown that an arbitrary stochastic process may be considered as a process on a suitable Ω in which the outcome functions f n are coordinate functions.
John G. Kemeny +2 more
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1960
To begin with, we assume that the M. C. {x t , t∈T} is Borel measurable. Using the notation of § 8, we may define a family of random variables {ξ t , t∈T} on the triple (Δ, Δℱ, P(·|Δ)) as follows: $${{\xi }_{t}}\left( \omega \right)=\xi \left( t,\omega \right)=x\left( \alpha \left( \omega \right)+t,\omega \right)$$ (1) .
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To begin with, we assume that the M. C. {x t , t∈T} is Borel measurable. Using the notation of § 8, we may define a family of random variables {ξ t , t∈T} on the triple (Δ, Δℱ, P(·|Δ)) as follows: $${{\xi }_{t}}\left( \omega \right)=\xi \left( t,\omega \right)=x\left( \alpha \left( \omega \right)+t,\omega \right)$$ (1) .
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Preserving the Markov Property of Reduced Reversible Markov Chains
AIP Conference Proceedings, 2008The computation of essential dynamics of molecular systems by conformation dynamics turned out to be very successful. This approach is based on Markov chain Monte Carlo simulations. Conformation dynamics aims at decomposing the state space of the system into metastable subsets.
Marcus Weber, Susanna Kube
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Asymptotic properties of interactive markov chains
Communications in Statistics. Stochastic Models, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1984
Most of the reliability models discussed in this book assume that the systems under consideration exhibit stationary Markov properties. To test whether this assumption is valid or not requires the use of various Chi Square and maximum likelihood statistical techniques.
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Most of the reliability models discussed in this book assume that the systems under consideration exhibit stationary Markov properties. To test whether this assumption is valid or not requires the use of various Chi Square and maximum likelihood statistical techniques.
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